{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Categories for Quantum\n", "\n", "Alexis Toumi & Giovanni de Felice\n", "\n", "_5th May 2021, Tallcat_\n", "\n", "1. Categorical quantum mechanics\n", " * the miracle of scalars\n", " * the way of the dagger\n", " * braids and symmetry\n", " * compact closed categories\n", " * special commutative Frobenius algebras\n", " * bialgebras & Hopf algebras\n", "2. Qubit quantum computing\n", " * the circuit model\n", " * the ZX-calculus\n", "3. Applications\n", " * optimisation\n", " * compilation\n", " * extraction\n", " * natural language processing\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Categorical quantum mechanics\n", "\n", "The traditional formulation of quantum theory happens in $\\mathbf{Hilb}$, the monoidal category of Hilbert spaces and bounded linear maps with the tensor product.\n", "\n", "Categorical quantum mechanics (CQM) seeks to make explicit precisely what structure is needed of $\\mathbf{Hilb}$ in order to recover quantum theory.\n", "\n", "**References:**\n", "\n", "* _A categorical semantics of quantum protocols_, Abramsky & Coecke ([arXiv:0402130](https://arxiv.org/abs/quant-ph/0402130))\n", "* _Categorical quantum mechanics_, Abramsky & Coecke ([arXiv:0808.1023](http://arxiv.org/abs/0808.1023))\n", "* _Picturing quantum processes: a first course in quantum theory and diagrammatic reasoning_, Coecke & Kissinger (2017)\n", "* _Categories for quantum theory: an introduction_, Heunen & Vicary (2019)\n", "\n", "In the process, we get a diagrammatic language for quantum processes.\n", "\n", "We also get a new intuition for monoidal categories:\n", "\n", "* **Systems** are objects $A, B$, composition of systems is given by their tensor product $A \\otimes B$.\n", "* **Processes** are arrows $f : A \\to B$, $g : B \\to C$, with their sequential and parallel compositions $g \\circ f$ and $f \\otimes g$.\n", "* **States** are arrows from the unit $v : 1 \\to A$.\n", "* **Effects** are arrows into the unit $e : A \\to 1$.\n", "* **Scalars** are endomorphisms of the unit $s : 1 \\to 1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The miracle of scalars\n", "\n", "**Lemma:** Tensoring with a scalar is a natural transformation.\n", "\n", "_Proof:_" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from discopy.monoidal import Ty, Box\n", "from discopy.drawing import Equation\n", "\n", "x, y, z = Ty(*\"xyz\")\n", "f, g = Box('f', x, y), Box('g', y, z)\n", "a, b, c, d = (Box(x, Ty(), Ty()) for x in 'abcd')\n", "\n", "assert a @ x >> f == (f >> a @ y).normal_form()\n", "Equation(a @ x >> f, f >> a @ y).draw(figsize=(5, 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Lemma:** In a monoidal category, scalars form a commutative monoid.\n", "\n", "_Proof:_ Eckmann-Hilton argument." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from discopy import drawing\n", "\n", "assert (a @ b).interchange(0, 1) == b @ a\n", "assert (a @ b).interchange(0, 1).interchange(0, 1) == a @ b\n", "\n", "drawing.to_gif(a @ b, b @ a, loop=True, figsize=(.5, 1), path='../_static/monoidal/Eckmann-Hilton.gif')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Definition:** A monoidal category is enriched in commutative monoids (com.mon. enriched) if every homset is a commutative monoid such that composition and tensor are monoid homomorphisms.\n", "\n", "$$\n", "(f + f') \\otimes (g + g') = (f \\otimes g) + (f' \\otimes g) + (f \\otimes g') + (f' \\otimes g')\n", "$$\n", "$$\n", "(f + f') \\circ (g + g') = (f \\circ g) + (f' \\circ g) + (f \\circ g') + (f' \\circ g')\n", "$$\n", "$$0 \\otimes f = 0 \\circ f = 0 = f \\circ 0 = f \\otimes 0$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "from discopy.monoidal import Sum\n", "\n", "zero = Sum((), Ty(), Ty())\n", "\n", "assert zero + a == Sum((a, )) == a + zero\n", "assert (a + b) + c == a + b + c == a + (b + c)\n", "assert (a + b) @ (c + d) == (a @ c) + (a @ d) + (b @ c) + (b @ d)\n", "assert (a + b) >> (c + d) == (a >> c) + (a >> d) + (b >> c) + (b >> d)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Lemma:** In a com.mon. enriched monoidal category, the scalars form a commutative semiring.\n", "\n", "**Definition:** A commutative semiring is a com.mon. enriched monoidal category with one object.\n", "\n", "**Lemma:** Given a commutative semiring $\\mathbb{S}$, the category $\\mathbf{Mat}_\\mathbb{S}$ of $\\mathbb{S}$-valued matrices is monoidal with the Kronecker product.\n", "\n", "**Lemma:** $\\mathbf{FHilb} \\simeq \\mathbf{Mat}_\\mathbb{C}$.\n", "\n", "**Lemma:** $\\mathbf{FRel} \\simeq \\mathbf{Mat}_\\mathbb{B}$.\n", "\n", "Com.mon. enrichment allows us to talk about **superposition**, **basis** and **dimension** in an abstract setting.\n", "\n", "**Definition:** Given two states $v, w : 1 \\to A$, their superposition is a linear combination $a \\otimes v + b \\otimes w : 1 \\to A$ for two scalars $a, b : 1 \\to 1$.\n", "\n", "**Definition:** A basis for $A$ is a minimal set of states $\\{\\vert i \\rangle : 1 \\to A\\}$ such that every state $w : 1 \\to A$ is a linear combination $w = \\sum_i a_i \\otimes \\vert i \\rangle$ for some scalars $a_i : 1 \\to 1$.\n", "\n", "**Definition:** The dimension of a system is the cardinality of its smallest basis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The way of the dagger" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Definition:** A dagger is a contravariant involutive identity-on-objects monoidal functor.\n", "\n", "In terms of diagrams, the dagger is the vertical reflexion.\n", "\n", "We may draw asymmetric boxes to distinguish a generator from its dagger." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Equation(f, f[::-1], symbol=\"$\\mapsto$\").draw(asymmetry=.25, figsize=(3, 1))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from discopy.monoidal import Id\n", "\n", "assert Id(x)[::-1] == Id(x)\n", "assert (f >> g)[::-1] == g[::-1] >> f[::-1]\n", "assert (f @ g)[::-1].normal_form() == f[::-1] @ g[::-1]\n", "\n", "Equation((f @ g)[::-1], f[::-1] @ g[::-1]).draw(figsize=(5, 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dagger allows us to formulate the notion of inner product in an abstract setting.\n", "\n", "**Definition:** The inner product of two states $w, w' : 1 \\to A$ is the scalar $w^\\dagger \\circ w' : 1 \\to 1$.\n", "\n", "**Definition:** The squared norm of a state $w : 1 \\to A$ is the scalar $w^\\dagger \\circ w$. It is normalised when it has norm $1$, the identity of the monoidal unit.\n", "\n", "**Definition:** Two states $w, w' : 1 \\to A$ are orthogonal when $w^\\dagger \\circ w' = 0$.\n", "\n", "**Definition:** An isometry is a norm-preserving process $f : A \\to B$, i.e. $f^\\dagger \\circ f = \\text{id}_A$.\n", "\n", "**Definition:** A unitary is an isomorphism $f : A \\to B$ with inverse $f^\\dagger$, i.e. $f^\\dagger \\circ f = \\text{id}_A$ and $f \\circ f^\\dagger = \\text{id}_B$.\n", "\n", "**Definition:** A basis is orthonormal if $\\langle i | j \\rangle = \\delta_{ij}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It also allows us to talk about quantum measurements, the Born rule and even a simple form of Heisenberg's uncertainty principle!\n", "\n", "**Definition:** A projector is a process $p : A \\to A$ such that $p = p^\\dagger$ and $p \\circ p = \\text{id}_A$.\n", "\n", "**Example:** Take $w \\circ w^\\dagger : A \\to A$ for any normalised state $w : 1 \\to A$.\n", "\n", "**Definition:** A (projection-valued) measurement is a set of projectors $\\{p_i : A \\to A\\}$ such that $\\sum p_i = \\text{id}_A$.\n", "\n", "**Example:** Take an orthonormal basis $\\{\\vert i \\rangle\\}$ then $\\{\\vert i \\rangle \\langle i \\vert\\}$ is a measurement.\n", "\n", "**Lemma:** A measurement is a choice of basis and a partition of it.\n", "\n", "**Definition (Born rule):** Given a normalised state $w : 1 \\to A$ and a measurement $\\{p_i : A \\to A\\}$, the probability of measuring outcome $i$ and getting the state $p_i(w)$ as a result is $P(i \\vert w) = w^\\dagger \\circ p_i \\circ w$.\n", "\n", "**Example:** Take $p_i = v \\circ v^\\dagger$ then we get the squared amplitude $P(v \\vert w) = \\langle w \\vert v \\rangle^2$.\n", "\n", "**Definition:** Two bases are complementary (a.k.a. mutually unbiased) if $P(i \\vert j) = P(i' \\vert j')$ for all $i, i'$ and $j, j'$.\n", "\n", "**Example:** Take $\\{\\vert 0 \\rangle, \\vert 1 \\rangle\\}$ and $\\{\\vert + \\rangle, \\vert - \\rangle\\}$ the two bases of $\\mathbb{C}^2$ with:\n", "\n", "$$\\vert + \\rangle = \\frac{\\vert 0 \\rangle + \\vert 1 \\rangle}{\\sqrt{2}}\n", "\\quad and \\quad\n", "\\vert - \\rangle = \\frac{\\vert 0 \\rangle - \\vert 1 \\rangle}{\\sqrt{2}}\n", "$$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Braids and symmetry\n", "\n", "**Definition:** A (strict) monoidal category is braided if for every objects $A, B$ we have swaps:" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2018.53.03.png": { "image/png": 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" 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" 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" 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" 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Definition:** A braided monoidal category is symmetric if\n", "![Screenshot%202021-05-04%20at%2018.59.19.png](attachment:Screenshot%202021-05-04%20at%2018.59.19.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2021.50.08.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "or equivalently\n", "![Screenshot%202021-05-04%20at%2021.50.08.png](attachment:Screenshot%202021-05-04%20at%2021.50.08.png)" ] }, { "attachments": { "Screenshot%202021-05-05%20at%2012.26.22.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Lemma:** In a braided monoidal category, we can prove the Yang-Baxter equation.\n", "![Screenshot%202021-05-05%20at%2012.26.22.png](attachment:Screenshot%202021-05-05%20at%2012.26.22.png)\n", "_Proof:_ Naturality + Hexagon." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compact closed categories\n", "\n", "**Recall:** In a right-rigid monoidal category, for every $L$ there is a right adjoint $R$ and a pair of arrows:" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2018.40.32.png": { "image/png": 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" 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" 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Lemma:** In a braided monoidal category, left and right adjoints collapse.\n", "\n", "_Proof:_ Define\n", "![Screenshot%202021-05-04%20at%2019.09.27.png](attachment:Screenshot%202021-05-04%20at%2019.09.27.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2019.10.04.png": { "image/png": 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KqBHV1tU/a4xodmk1apfr5OrG6/noWxgoGHIaIYzeGz8zuWKabxZt7mShYslmuWL1xvqeTa1tvl2SfaCDo6O+k7yzgAvJFeu67PbRfcSj2/OOV/3Os97Hdh3ySfal+lHIvv4eAU6B9kE2wZYUyxCzUM0w2XCBCJbdNJGIyNWoH9Sf0Wux6DhivFCCxh6nxOikwuSWvVMpNPv5UmXStA/YpPsdjM84fKgysy1rOPt7LvNhhSP2eRFHD+fXFTw69u74eiFnkXKx3cnQkoOlZ041n+4tmznz6xxzucR57Qq7C+TK2KpD1cXwOdddN3eJeFmx3vFK1NW8a3UNnddHbnxpwjRz3JS8pXHbosXtTmBrTFvK3dT2Ax0H72V0Hrqf+SD7Ye6jw12HHx9+crg792nOs6yeQ73pfan9e5/H/RU1sHsw8kXMUNLLg8PHXpWPNLx+MPryzadx8JY4IfhOflJnynzab+bs+08flWeTPrV+/jWvuRD35fLXd4vsS5bfU340/Jxe4V51WMv+1bk9/8YIfeQO5GdUO/oQxhErjl3A3cRnEBxouGlGac/ThdOrMyAY2hnTmSyIDMRe0lFmWxYGlqes2Wwm7BB7M0cEpxDnEFcOtw73J55SXjPeb3xl/Gb8nwWOC2oIjgjtFeYXbhXxFlkVLRZTEusWDxBflTgmKSXZJuUoNSWdKiMiMySbu8Ngxze5KnlPBTqFNsVIJQGlfuU0FQWVcdU8NW21T+qlGuYai5rntey1fmnX6bjrYnVv6JH1ifp3DSIN+Q17jdKMlYynTUpMbeH3jtvmURZSFu8sy6w8rFmtn9sU2DrYkewG7U86eDsKO35wuuqc6GLsyuA67FbpHu1h4EnrOeh1Zmewt4L3yq77Pvm+Xn4SfkvkTv9jAb6BikGooMHgWkpKiFOodBg67E34rYji3fGRrlEaVN5oVPRszEBse1x9fFlC3p7UxPik0GT/vTv3uaU47XdItU+zP+CQ7nTQPWPnoYDM0Kzo7JSczNyCw2VHavIaj97L7ysYPfb5BKpQosir+OjJ+yUrp2RP+5WdOPP47Gq5wvmAipILPVWoaq2a+Nr6uo+XJC+H1Ndembum0rD/encjR1NYc+ctvtspLW9brdpa2uU7LnZK3b/60ODR8OOEbr6nvT2H+5yeiw6AwY9D74Y/vAZvRMZ3TdROoWcSP4JPFfPkr7pLaj+dV4s35n/rv7+NglEB4MQhADb+z3GoASD3IgBiewBgg3NPOzoAnNQBQsAUQIsdALLQ/nN/QHDiSQAkwAMkgRowg/PLMDinLAL1oAtMgDWIHVKGHKFo6ATUDL2Gcz5phAsiFVGPGEUyIA2Q8chLyCk4S/NClaJewZmYD/oC+hNGBZOKeYblwYZj23AkHAXXjufEx+L7CYqEIsIqDZnmKa06bTUdO10uPYI+if47QyzDEmMiE8SUTWQlVpDUSL3MISxYlgusxqxTbJnsUuy9HDGcHJytXP7cNNzXeDx4kbyX+DzhjKBPIE/QVohJ6LlwkYinqIDolNhF8WgJDUlIsksqX9oTXp3zsv07WuQq5QsU9ilSlByVNVT4VCHVMbUW9eMaIZraWvRaI9o1OjG6uno4vT79BoPrhk1Gt4xbTe6Zdpn1mA9ajFpOWy1Yr9ji7FjtRR3UHK2cyM7JLsWurW4zHiRPfa/IneXeAz4EX32/JHKz//dAtaCk4PYQQqhzWEX44m6zyLKouWitmJzY0XilhKN7FpJckx/s005pTbVMm0jPytDOBFl9OVcOn8oryDc7hjx+vzC/OKDE8JR0meBZkXKlCpvKqOrS2ieXQL3qVZsG9xvBTck3T9y+dqe/bamDt9PsQcyjs4+fda/1yPTtfH5k4O4QaZg8cml0dpx7Qm1Sb1r+Pf2HF7NHPu+Ya18w+9L5TWGxZGn5h/3PC8sLqxprKb/ubp4fW/NPhOdfAqgCE+AKQsA+cBzUgU4wCn5AJEgOsoEioKNQA/QSARAScJafhriKeAvn8VbIdGQbcgWljTqA6kazowPRjRg8xhvTiGXEhmGf4KRxebhFvBf+AUGWUESDpImiGad1pn1MZ0jXSq9FfwfOYh8x2jOOwnnqOvE4SZb0lDkCzjybWX3ZaNia2QM5WDkecu7hkuYa5y7iseXF8Xbw7ec3EMAIPBUsFPIVlhVeFekWLROLEjeW4JL4IvlY6rx0ioynrOYOCTl2ebz8qsKc4oTSC+XHKrdVL6qVqB/SoGp6ahlqS+ow6izqDuu16tcbXDVsMGoyvm3SZtpp9ti81+KF5RuraesFmxU7nD2rg5ijupO1s7/LXtcSt5vuwx5rXoI7Lbxjdp316fGDyCr+EQE1gVPBopSQkKuhy+GmEYW7Z6K0qHuj22JRcVbxRQlTiepJR5Kn9xmnVKfSp+05MA2fJ72ZFlkPc8xyu4845I3lpxzjPX63MLCY/mRzqf9pUtmDs3vLVc5/uXC1KrZGqw5zceDyhSvJ17yuqzTSN03cvH77wB2bNva74x01ndQHWo+wXYNPap7u7/Hq03kuMsA0+GjI+eXkq8TXzKPXxpzGVyeqJ92nGWa6PmTOWn5mnHuxcPZryKLKd8SPnuXS1aBfitvzjwQYQLt5AogDFXgFuIFwcBCcAbfBMLz/BSELKBaqgAYRNAgjeOd3IHFIe+QZ5BeUBaoKjUdT0W8wTvBut8EO4Mi4n/hCgjphkuYkrR7tCF0SPT99F0M8oyTjBNMZoh9JgvSd+SFLGWsSmye7HocUJzsXDTeCe5VnmXeVHwhg4TdQHmFZEW1RB7Eg8f0SJyVvwHn3vCzjDgU5V/l9ChWKPUorKhKq7moF6v2azFru2hU6c3ra+ocN3hgpGueYjJtpmRdafLGys75kS2sXZv/YUdIpx/mDq4VbrQfek+L10Ft010GfST9DcmUAMtA/6B5FNCQjdCbcKqI+kiUqgToWYxR7OZ49Yd+ej0lu8D5VSalK5Ug7ko46mJzxJdMj62r2eq7T4aojy0cd8y8fIxynnHhQJFWce3Ku1PXUnTLRM/nw2e9/vvuCZmVVNVNNYu3URcdLLfWiV/KuLjV4X3/QKNN0tHn+lv3ty3cIrYFtre3EjoB7jfdRD+welj6aeCzxhNJd+XS8h7PXvu9g//XnbwcIg3IvHIaoL48M17y6NzLwemp04c3qOPQWO4F5h5kEk8tTn6ZHZ56+b/5Q/jFzNuKT9WepOezcm/nmhawvHl8lvn751rKYtmT0HfO980fKT82fC8sXVjxWCauNa+RfdL+urbtvzH90oKLC5vUB0RoAgB5dX/8qCgC2AIC1/PX1lfL19bXzcLIxAsDdsK3vSZt3DSMAZ7k2UN+V9wL//paz9a3pH3nMv1uweRNtaoVvos0WvpXAfwEtFt65uwJTwAAAAFZlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA5KGAAcAAAASAAAARKACAAQAAAABAAABWKADAAQAAAABAAAAmwAAAABBU0NJSQAAAFNjcmVlbnNob3TxbHpnAAAB1mlUWHRYTUw6Y29tLmFkb2JlLnhtcAAAAAAAPHg6eG1wbWV0YSB4bWxuczp4PSJhZG9iZTpuczptZXRhLyIgeDp4bXB0az0iWE1QIENvcmUgNS40LjAiPgogICA8cmRmOlJERiB4bWxuczpyZGY9Imh0dHA6Ly93d3cudzMub3JnLzE5OTkvMDIvMjItcmRmLXN5bnRheC1ucyMiPgogICAgICA8cmRmOkRlc2NyaXB0aW9uIHJkZjphYm91dD0iIgogICAgICAgICAgICB4bWxuczpleGlmPSJodHRwOi8vbnMuYWRvYmUuY29tL2V4aWYvMS4wLyI+CiAgICAgICAgIDxleGlmOlBpeGVsWERpbWVuc2lvbj4zNDQ8L2V4aWY6UGl4ZWxYRGltZW5zaW9uPgogICAgICAgICA8ZXhpZjpVc2VyQ29tbWVudD5TY3JlZW5zaG90PC9leGlmOlVzZXJDb21tZW50PgogICAgICAgICA8ZXhpZjpQaXhlbFlEaW1lbnNpb24+MTU1PC9leGlmOlBpeGVsWURpbWVuc2lvbj4KICAgICAgPC9yZGY6RGVzY3JpcHRpb24+CiAgIDwvcmRmOlJERj4KPC94OnhtcG1ldGE+CgvQ/2wAACQ9SURBVHgB7Z0LuFRl1cdfTLtJ3oAoREUDUxMphAAlwCQ0DFAx0KioAA3MgEolFE0hVEgzFbVUwAsSmQJeQATREBUERRAMgcRAwSxFFE3N3N/6rZ4533DmcM6ZM7Nnrz1nrec5Z2b27Hn32v+9Z837rst/NYhEgosj4Ag4Ao5A0RHYregj+oCOgCPgCDgCioAbWL8RHAFHwBGICQE3sDEB68M6Ao6AI+AG1u8BR8ARcARiQsANbEzA+rCOgCPgCLiB9XvAEXAEHIGYEHADGxOwPqwj4Ag4AuYM7I4dO8Lzzz/vV8YRcAQcgdQjYM7ALlmyJLRt2zb1wPoJOAKOgCNgzsD6JXEEHIHiI/Df//43fPDBB8UfOMER33///fDRRx8lqEHNh3YDWzNGvocjkHoEJk2aFDp27Jj688g+gb333jssXLgwe5O5525gzV0SV8gRcATKBQE3sOVyJf08HAFHwBwCu5vTqIwVwgf28ssvh02bNoXNmzdXPPL8E5/4RDjwwAPDAQccsNPj5z73ubDbbv47WMa3hZ9aGSPgBrYEF/fJJ58MN9xwQ5gxY4YGGvbdd9/QrFmzir82bdoEHPZbtmwJK1as0Eeev/vuu6Fx48bhzDPPDEOGDAktWrQogbZ+CEfAESgWAm5gi4VkpXGIbs6cOTNcccUV4emnnw7du3cP11xzTTjppJNC8+bNK+2d+xKa3lWrVoX7779fDTPjnHrqqeG8884L7dq1y/2Ab3EEHAFzCPjaM4ZL8uijj2ou7/e//301hmvXrg3z5s0LZ511Vq2MKyo1aNAgMLO94IIL1NDOnz9fZ7QdOnQIp512Wti4cWMMmvuQjoAjUEwEzBnYp556SpfLxTzJUo31n//8J4wcOTIcf/zx4Stf+UrYsGFDuP7660OrVq0KVuG4447T2SyFGFu3bg2tW7cO06ZNK3hcH8ARcATiQ8Cci4BlMfLqq68GAjxpEfylffv2DcuXLw9z584NPXr0iEX19u3bh8WLF6vrYeDAgeHFF18MY8aMieVYPqgj4AgUhoC5GSzLaeSOO+4o7MxK+On33nsv9O7dO/z1r38NTzzxRGzGNXNKuA9GjRoV7rrrrvDrX/86XHzxxZm3/NERqBKBZcuWhRdeeKHK93xjfAiYMrC33XZbwMDuvvvuYdy4cTo7i+/UizMywazvfe97evM+8sgjRXEH1FazU045RY3sZZddplkKtf2c71f/EFiwYIH68OvfmSd7xmYMbCYIRADnYx/7WGjZsmXo2bOnpiwlC1H1R58wYUJ48MEHwwMPPBAOPvjg6neO4d1evXoFyiCHDx8eSAdzcQQqI8AkIMND4PdIZXTifW3CwE6ePDn06dMnnHjiieG73/2unjHLX3JDjznmmLBy5cp4Uajj6KtXrw4XXXSRBrKOOuqoOo5S+MfIkT3jjDMCPlncFS6OQDYC/AATgCWnesSIEfo8+31/Hh8CJgzslVdeGcaOHRv+/Oc/q3uA02U2SEYBBvamm26KD4ECRv7FL36hGQO4CJKWq6++Orz55pvhuuuuS1oVP74hBObMmRO4T7/xjW9o0HjNmjVh0KBB5lmoDEFYkComsgi46FVJkyZNwp133lnVW4lve/bZZ8NDDz2kRQSJKyMKUB127rnnhquuukrdBXvssYcFtVyHBBFgZThs2DANwB577LGaO02co3///uHtt98Ot99+e2jYsGGCGpb/oU3MYNMIM7Pqzp07a76rFf1xFWzfvj3cd999VlRyPRJC4F//+lcYOnRouPDCC8P06dMr+CyoBoTi77nnngu///3vE9Ku/hzWxAw2bXB/+OGH4U9/+pPmolrSfZ999lFf9h//+Ectq7Wkm+tSWgTwt77++utVzlC/9rWvBVaNTiIU/zXxGWwdMMY3vG3bNl161eHjsX6E1C0yMghquNRvBKpb/sPe5m6k+O8PN7B1wPgvf/lLIGuAWYI1+frXv67+NXzELo6AI5AsAm5g64A/ea9wDViRf/zjH2HKlCkB10WjRo00AyNjYMmBhLPg73//uxV1XQ9HoN4g4Aa2Dpd60aJFYf369XX4ZDwfeeutt5RkpmvXrkoEc+ihhyrRzBtvvKHFGvDJ/vOf/4zn4D6qI+AI7BIBN7C7hKbqN+AbQOADsCKwdcGBQLcE8h1Jb2NWS5UXBN7QJzqHrJWr5XrUJwQ8iyDPq01pLNHXZ555RmeFGDMLcsQRR2j6TadOnZQXgTbN69atC4899pjyylrQ0XVwBOobAuZmsDD5W5odZt8QpD+RqP3pT386fP7znw8QauP3tCJf+MIXNLcR/ytlvFTIQdrt4gg4AskgYM7AAgNG1ppgXKn1pzKGwNE555wTHn74Ya2KsVT/T5oWxB7wOPzoRz+yBqPr4wjUKwTMGVioCi3NCrkb/vCHP4QBAwaEwYMHaykq+YMtpAEhFVNQFNJvy5rO6A0rmYsj4Agkh4A5HywJ0PgPMVgYWwuy//77h9mzZ4dvfetbqs7ee++txCqQvNCBgdkts1orQjsZas9dHAFHIFkEbFiwLAz23HNPfUULlr322ivrneSe0gk2W2hlQ18shA6xsBVZESq4/va3v2mnAys6uR6OQH1FwJyL4DOf+YxeC3I7rcohhxyiRsyifkuXLlVOWGgeXRwBRyBZBMwZWGj3EJLkrcqXvvQldQ1Y1G/WrFmhY8eOWtFlUT/XyRGoTwiYM7AwQhFEgm7NqtDZlVQoIvWWBPcA/Ll0N3BxBByB5BEwZ2DJgf3sZz+rbbuTh6dqDVh+E4ijesqSQKEIkXKm7Y4l3VwXR6A+ImDOwHIRiNpT9mlV8BMTpafRoRXB4NPC+6yzzgqsAlwcAUcgeQRMGtiDDjrIPPsTzPD0ELNSFHHzzTdrB97zzz8/+bvKNXAEHAFFwKSBJUr/4osvmr5E/fr1U4NGoUHSArHL6NGjw8UXX6xEL0nr48d3BByB/yFg0sDCDgVRiWVp2rSpdjS44YYbElcTOsKWLVtq+W7iyrgCjoAjUIGAuUIDNDvssMPURfDvf/87fOpTn6pQ1tqT4cOHh+OOO05zYiFaSUJ+97vfKYvW008/babyLQkc/JiOgEUETM5gyTOl9PT555+3iFmFTjSPI+d0/PjxFdtK+QSeV1p10x0Ukm0XR8ARsIWASQNLFJxAV6btiS3Idtbm0ksvVQrDDBH3zu/G94rj9e3bVzsZfOc734nvQGU0MpkW5FfjfqJxJZSOW7Zs0cq3MjpNPxVDCJh0EYBP27ZtA8veQYMGGYIrVxWaDNJF4Gc/+1mYO3du7g4xbKG/1gknnKDHveyyy2I4QnkMiUFdvny5dtl96KGH1KjuqtsuLp4ePXoorrh9rPBglMeVqL9nYXIGy+Xo0KFDWLJkSSquzG9/+9tAp1loDeOWTZs2BYz6kUceqTNn722fi/g777yjZOOsgjp37qwGFsxgPaM4ZOPGjQEyoVdffVVb6syZMyeMGDFCX//whz/UQhe4dDds2JA7uG9xBPJBQPI4Tcrjjz8eCZ9ptG3bNpP6VVbqxhtvjD75yU9Gy5Ytq/xW0V7L0jYSoxHJ7DUSA1G0cctlIJmxRrfccksk3Sb0b+LEidFrr72W1+nJDDcSPodIDHMkdJnRT37yk0gaRuY1hsWdJRgaSSdki6rVWSehNo3mz59f58+X4oMkypsUYeWPZJkW3X333Sb1q0opmf1EUoUWbd68uaq3C9omPsNISogj6VgQSQeFgsYqxw/z4yMlzFHDhg0j8YtHMost+DSFUD06/PDDo8aNG0cy+y14vCQHcAObDPpmXQQQvuDbvP/++/OZkCe6Lzmx5PCeeOKJ4fXXXy+aLvIjE7p16xZoB3PXXXcFSMld/h+Be++9V332cAmvWbMmjBkzRvum/f8edXsGwfrKlSvD2WefHSBX59Fi54q6nZ1/qhQImDWwnPzJJ58c+PLsKjBRCoDyOQaGD7pAHglCiXsjn4/n7Mt5jxo1Kpx++unhV7/6VRA3hLeBqYQSPzhkU+BDnTdvXjjwwAMr7VHYS37owV6WomHGjBlKpGOpe0VhZ+efjhsB0wa2d+/eGowgApwWoZ0M+hLBJhpNGWtdhK4E5NlOmTJFSWXId3XZGQFakjOzhORm7NixsXYj7tq1qxZ0YMQtdbDYGRF/ZQ0B0waWVJk+ffqokbEGXHX6NGrUSL+MtPcmip1vNFoCNUECEsqKxRKV9CGXnREQP7fOXIn2n3feeTu/GdOro446Sgl+rrvuujB16tSYjuLDlhMCpg0sQJMHi5sg0wMrLeDTmYFlpQRJQqdOnTSNqybdOcdevXopp8C4ceM0r5b+Xy47I8DqgOIKqtcoFS6lHH/88eGKK65Qf2ypi0tKeZ5+rOIgYN7AckOTBI7/MW1C0GXmzJm6jP3mN78ZFi1aVOUpSHxTZ0SUCFNp9Mwzz4Sf/vSnsS55q1QkJRuvueYabdkzbdo07X5RarXx93bp0iUwe3Z/bKnRT9nxkkleyO+o5JiSKlOM1Jv8jly8vaXHWJWDifsg6t69eyTuhOg3v/lNJFHqKvfzjf9DQIoDIiE8j2SZnigkUk0XyQ9oNHny5ET1qO3BPU2rtkgVdz/zM1h+rwYOHKhMUZCapFUyzRwz+kuerwZnWrdurZtWrVoVfv7znyeeJXDVVVep/xilWIovXrw4rF27NqN2ziPNKe+5556c9jnr168PtLChrBeB3xdf6SuvvJIzRj4bJkyYoB0vfvzjH+fzsaLvS7YC5dGXXHJJarJcigHCgw8+GK699lodaseOHRqAffjhh6vEYPv27QG+5Mzfc889p59jdQYXRL2Q4trr+EaTL34kHKyRXNT4DlKikSUSHX3xi1/U87n99tsjWWaW6Mi7PgwzZ+GVjcTfrTutWLEikq4N0cEHHxxNmjSpyg8uWLAgkqVyJCXCkbg3ogsvvFD3mz17diSlzpGkNUVt2rSJxDWi2+ULFgnHRCQ5wlWOV9NG6TemxSe33nprTbuW5H1WJcxi01CEUIwZrHTN0GtMxZz8gOq1vemmmyLJV48kVS4Hc8nyiMS9F0lcQf8krqD7UJ3JfUO1ZiHilVyFoFfps5SGNm/eXKt0Kr2VmpeSehVJbq+WYJ5zzjmmyoAp8eWLUFkGDBiwSwOL60b8ofoRjCnXB8HYyqxWn19//fWRpKvpc/5hhCVIVPE6nycSuY9kJWCqkk38sJEUluRzGonsW6iBxahSpp1xYT355JOREA3puQihTiS8zTnnhYGVlLac7Wzgx1niElW+V9uNaTCwqXARsJSAeJvIOktEUnTSJG+99ZYWDBDEevPNN5UljECNpeaEsE4RuMlHaLAoPxT6EZaDdFWAJJ1qKs4VOeKII5TRSl/IP47BkrIuQg80eqFRyGFFaJHO+RRaVGLlfHalBxSPEAwJP4juAg8yRTBkUpC2BklOVcL7ZHpQkZkdECTHG9dBuUtqDCwXgqRychGFgCMV14VKLJnBafksFUd33HGH3lScQ7aw3+WXXx6k9j17c0mfY2AlkFinY+KHxXeLjzxjaIRwRcfikVbimRJTjlEXPyyGG0NGdZ8loYSZbBEKEMpZdnV/wCQH6x3XWWaeO0FAZxJayDOpGDlyZBgyZEjF+x//+McDf2TNlLOkysBCzSc+H62UspzozY3GbItffFkSa3CH7gyUdFYlwtqkASVmZxB4V75Rq/pMsbdhADNGMJ+x+YJg9PiikZcqhDQ6y8kUV/DYpEmTinY2BM4oxMhXoBlEPwyaJeHaQYVY11m5pXOpTpdd3R9QdGJ8yQ0Wv/1OQ/BjSpk3zThZsVFqnC3MhiUjJHtT2T1PlYEFfZackEyzNK0uup3UlaK4AC5bZttUoWFgyA6oblnboEGDcMEFF2jO7JVXXqm/+u+//35JT0H8a8ruX9NBhbpPMwvYD/xPO+00/fJAcIOR5XzJXSaXF+FLBy9DRpi9gk++goGFhF3YsvL9aOz7s9xFv3KWyvcH5PK33XabnjIrFIwlmRXZ9wf7ZO4DfoghQspIxqVU3fcis2+qH2vrULa0H1F3gkVQycmFMqEakXKZXWkAa/DgwXWmLJR0rUhuVB1LllYlOzcpydXIf/YBZUkXHXDAAdFXv/rViIAWIoxhkfha9Tn4y4+DBjgIcsDfi/4yW4/at28f8Xnx1UVCEq77849tdaGghKZx2LBhFeNYesK159wtc/QWGuSSH3wNcpEBgJAJw/WXSksN8mXygbPvD/K6CXCKrz4iGEgWSUakSCQi0FuIpCHIZZYPtibgMaxcYCKR4sOsaffY3pc8UU1T4QtGxB1e0kLl5ZdfjiQ/VgmShSym0OFq/XnJ69Sob02GXfyhtRozm6iaLyhfvtGjR9cpLY1rnXRxwa5OWmZnOB8j6SG3q10S316ogeUE+GEUCseIbBiEiU5VKXfZ9wfZB5X5i8kgkBVeVNN9pgep5l8aDGzqXASZ5QJEMEQm6dtFNFuuQ+atkjzSIga+WqLi+BQpFCCIlb0MqqsiQtqt3AUEAWDkorVJKQT3BFwIMHlVJ9K5obq3K97LDprBKsZ5wXyFSyRfoWBBcnLz/Vhs+0taW5AcZr3vuP7cj5miCpa/YJkJ+MWmRIkHJkYgs9IK1xzXcb/99svRIvv+IG5S2Q1A0YnMeAPMc4UIWQlivAsZIv7PVvMDkYq3xMGuyecSpSyJviyNxOemS0IhHIkkJSm24zJLh6WfvNLs2WBsBzQ6MAUG8k2I5MfUjIZS0RQxgxI/eyRpeJEE+LTgglksxRmHHHJIlbO7pE6gGDPYpHSv6risWrkncD9YltTOYDM/PUcffbSmNxHNjJOnk8Z45P7Bck++J/l9kI0QdItLmBURKCAHuGfPnoHSxPoo5BEj4GFFCNzB+8tKpn///qqbuHY0wEfWBKlLVc3urOifdj0ypbakgJkWy9Y/H90effRR7cdEIAS/T7FEDKsGeWS5rqWk0pG0WEPXehxmr5TWipGtqKSp9YfLYEeIVeRLFL300kvmzgYfPM0umcHSVJDVRqG+xThOstxmsPiCCbDKj26ED9yq7G7a+uehHIzzpEiddNJJmrxMCkll308ew2lBADms5Pj94Ac/0F5YxW5HUlt98GU+8MADOoOGMAX/XikF3yIzMrmJa31YUqrIiy13OfbYY7UHGG1lwIeYQKG+xTgwy+fa1eb4Sd4TV199ta4eaOdD3jXFDBTpkJNsTexpVABCLOHhXGU5TQAKLtZ8k9oxqBLpVkYpclkJXFkIrsCJCzsV3Q3II+3Xr18BSOX3UYok6DWWz5eU4EZ9MLAgCTsUecwwplWu0ssP6fj2ploQg1QsSeqewLiSV05BDm2C4OaF1Yx87OnTp6s7rVjnWJRx5EtTdiLJ7JH4ZpXJJzv3rroThR1IjFYkhkGZgcTHWt3uib0HwYbMkEwul+MCxbKLIHPO8mWMxPeaeWnuEZIdeIfTLOPHj9fvJ23ZSRHLpGnJyjWSiZQGn4vpHiwGVqkPclX1K9OsWTOdybZr107btcADsCuhjp46achJXnvttSAsQVrmSh21RcFFQL8u2PTlBrCoYr3UieAnbiqrQpocy+k0C24n+Ilpy56d6ic/HAGuWVac1qSsXATZ4NJwkCUDeXv0b8JwUi9deZnEBaPMEe4AckCtC0tvmiJC1I2fGTLyuIVIeXU/UlUdHzcNf/VFpNrNNOELuad1KVHe1fVL4p7ILrmurBdkM9lkMpXfT+p12RpYAOVXjnbXUrYZoJVbunRpEHLkIOWfFXjTGhzDmv2LWPGm0SeSY6k+P+jiIJCJuz6fmY9UUuWFRn1r1gg+cDGwqrB4L+EzJVhbLPF7opZIFsPPkIYxtmzZEskSTnt7kXqVdqEcEc4C/FHlLmnwwQrJDf4aZfq3dj0ovUa31atXW1OtIH0yPtiCBon5w2Xpg63qt4UlBJRy0hZFZ6xEfetCz1fV2ElsoxwRXxQ8rOaTrZMAqMTHJMuDWbuw+Jf4yDUfjswaih7yXYXUPLLvURMCZW9gqVfOCJRq1MLDYQCvLDyeMrPNvJ26R/yvpAbBKO+SPALQNFLdZU3QCU4L/PcupUWgbBGHT5V8Vhz7lclS4C6Fp1RWB4FSWwJdaRQCdpQH0+XTPOlFGgHOU2d8+ZQ2l5rLtzo1WaUxoSDLwaX0CJSlgaWaBsMp3UfDRRddpEu3ytDC7LRw4UJNUGbmMXXq1Mq7pOI1gQu+RGRMuCSLAFkTJPRTdWdFmL3C5QD5u0vpESgrA0s7EhojdurUSXNFxalfbeoVM0Bmf7SzwDdLuWPahHQ0Gs4JIXbaVC87fWl/QkWR8N6aOTd0wbjiSnJJAIGYg2glG55Ic+fOnbWiQ3I28z4umQX0uD/77LOLShaTtyJ1+ABVZ5IatBNjfB2GMfuRNGQRZMCTFil6LSS3OrMpsUfoHbkvaLFdjuJZBCX6wYDo4ctf/rIWEUjrE51F5Hto6YygZDFQEA4dOjRVVVJUnZHoju4uySJAlR2zWKoDswOspdZKDKrqgO8Vjg6XZBBIvYtg4sSJAab14cOHB2lFoaz5dYUS1wLtl+l+CYFEmgROUqrRXJJHgOpBIWJX11NS2tBCna4LpPG5JIhAWpcOkDqwnBcfZJ2a6FV33lIGqI38aNqWFpFSSE0mj7PDQlJYpMlFkMFIDJzyxCbRhQGCI74XcMCWs6TBRcBSOHXywQcfRFL6qv7WuPxLQg2oHWLTVPVFY0Dhik3d9axJ4TQaWM6Je1TaXUeSJljTKRbtfcjZpeghklVdnZpLFk2REgyUBgObOhcBaTCnn366tuqgQiUu/9K3v/3tcP755ytDD61A0iCkm0lnhzSoWi90vPnmm0PTpk2VBD7T9ibOE3/nnXcC3BpkM5B2aJETIc7ztzh2qgwsQQOql2DXf+SRR2Lth8XFuuSSS/QYFll6qrqZJItCmcFk8lDV276txAiQQkcAll5qVFLF+UO9detW7QcG5SZ5uBhZl+QRSJWBJTJL4jStYUrBlk9pLSW1cBiIqyD5q1WDBmQSSJ/6ADWdiw0EYJ2C2o/GlWQYEEAtttC5g7H5YWVVBx+yiw0EUmNgqbfH2DEjiLOTa+XLIs0Gg7QG1rLbJNNuKutV1Wta20DqQRmwix0EcBNQNSgNOdXlBK/pqlWrClaQTAV60NE+CAJ2N64FQ1r0AVJhYOEKIG0KnxapVKUWmLfWrVunfalKfex8j0dPqGJ8efM9ru9fPQLSlVhdTuRpU0HIjJNYAuxb+bh02BeCeBr9tWnTRsukpbghSDuVgpp8Vq+9v1tXBMwTbm/btk07EjCLpDNBEgINHTOETM5tEjrU9pi0voFc2cUmAlAGQr7CpAGj2K1bNw2EwexGh9rmzZsHqDX5I0iFbxXGN+kzp4aVmTCvaepJ3jefd7GLgHkDi9+VNsgYtySFQgbcBRkimSR1qe7YVHV5JkF1CNl4j4Akfn16ZWEoiS1MmDAhSEpalTNaWsZ36dJFjTLGFQPsYh8B0wYWQ0HbbJZEEEwnKa1atdJI8OTJk5WpK0ldqjt2y5YtNcjFUtLTdKpDysZ7+GcHDBigf2gkOd5KoM7KDdlnn32UqAUXg0v6EDDrg8VA4HeFKYrouAWhayXN/2Dtsir065J2MjkcuFb1db12RgBDSuYBqyX+MMBuXHfGKE2vzBrYWbNmBWGJ0sCAFUBJ4mZmwYzaqtDQkZnrpk2brKroejkC9QYBswYWkgqKCizl9JECxWyaPFyrQr4l3J8ER1wcAUcgWQRMGti1a9dqlJW8QWtCoOHxxx+3ptZO+rCsJHji4gg4AskiYNLAQrt35JFHBnI6rUm7du0CeYeWpVGjRlrRZVlH180RqA8ImDSwpKxQoWJRqCKjTXblRoqWdCXy7K28LV0R16W+ImDOwBKhX758uSZdW7woLVq0ULXIV7QqEH28/fbbVtVzvRyBeoNA4gaWdCzKX+EZ4PlLL72kaUa4CKB4E1LtcO6555q5IASRIIGx7IeFxYlULRdHwBFIFoHEDSwpRXCv0geLclQo3diGETvmmGPC3XffHU455ZRkUco6OongzLJnz56dtdXWU/Im0dPFEXAEkkXARCUXBQXkb1LRgnGlaovnLHOZKQpDe7IoZR197ty5+sryEny33XYzXQyRBac/dQTKGgETBhaEmcVCFjxq1CjNNcUPu3TpUlPGlWX3L3/5S+X2lL5Hmg9LXbhF4YfKxRFwBJJFIHEXQfbp429lJgtBMe1aYIayIh9++KHOqqXnkc6wu3fvruxezlxl5Qq5Ho6APQRMGVjggScToe7fimzfvl17HdGKY9q0aRpAgj6RH4OuXbvqD4IVXV0PR8ARsIOAOQPbvn17RUc6RppBady4cWH9+vXhUWH3IuPhvffeU+NKX7CePXuGvn37us/TzNVyRRwBOwiYM7BnnnmmBros5ZnS0YAuARjXjF7wc8JTe+utt4bVq1dr1oOdy+qaOAKOgAUEzBlYcjhZelvybVIZRf4rgl6UojZp0qTi+tHxwMURcAQcgcoImDOwKNi2bduwbNmyyrqaeI1eGT+xCYVcCUfAETCLgEkDSzsNMgksCnqhn4sj4Ag4AjUhYNLA9ujRQ8m2N27cWJP+JX0fCkB6cqGfiyPgCDgCNSFg0sC2bt060FsK2kJLcs8992gLjw4dOlhSK0cXshyciyAHFt/gCJQcAZMGFhTOOOOMMHXq1JIDUt0B0Yde9pSiWpYZM2aEe++917KKrpsjUC8QMGspBg0aFNatWxfmzZtn4kLAiUCAizQy67Jjxw7rKrp+jkC9QMCsgT3ooIO0NHX06NHho48+SvRiQKMIR8Kpp54aDjvssER1qeng5ORm5LHHHss8TfXjli1bVP9XXnkl1efhytc/BMwaWC4FFVTMYq+99tpEr8zkyZOVBPzyyy9PVI+aDo7vlTbnmZbPQ4YMCZT5pl0yOdF0GXZxBNKEgGkD27x58zBx4kRlsFq5cmUiuL7wwgth5MiRYezYsRp4S0SJWhyUoBYzbBpGEoQ7/PDDwxtvvKGtd9JuZDMUkZnHWsDhuzgCJhAwbWBBCFIV+nNBug2TVSmFvlYnn3yy5r3CWWtVwAXSmSeeeCLcd999gZYxcDnMmTMnbNiwQYnLN23aZFX9avVasGBBmDVrlu4DyTmvXRyBtCBg3sDCazplypSw7777qqEtFdE1M8LevXtrxsCdd95pOnMA32SrVq3Cs88+G7p161Zx79EBd8WKFcqvm+FQqHgzBU8IKvbr1y/06dNHteWR10899VQKtHcVHQFBQAI4qZCtW7dGYkSijh07RjJji1Xnbdu2RTIjjITQJZKZX6zHimNw4dWN+vfvH8fQJRtz5syZkczEoy5dukTig424VdesWaPXpWHDhhHvu9RvBGSVFs2fP980COZnsJlfQQhVoAtkZglXQVxLxcWLF4ejjz5auytQFgvxjEvpEYClbMSIEYEW7nvuuacqwCNpe/jEed/FEbCOQGoMLEA2a9ZMe3T16tUrnHDCCVqMUKxy2s2bN4eBAweqL5Nl9pIlS0KLFi2sX7+y1U9mqOHSSy9VX3L2SeJbZjvvuzgC1hFIlYEFTGYxkyZNCsw08SuSlzp48OBQ1yCOuB7CsGHDwqGHHhpkCRoWLlwYbrnllrDXXntZv3aunyPgCBhHwEzTw3xxgvya6ipSd8aPH69BHvI/4THI/mOJn2kASEtwmhVm/5HW1KZNmzB9+nQNpmT2zVcf398RcAQcgcoIpNbAciIYQ1q28EdBwqJFi/TvxhtvrOg8AFH2fvvtFyRwFd599109f/JrJXgShg4dqo/Mgt2wVr41/LUj4AgUikCqDWz2ybPE5w93AUI6F+lL/JEn2rhxY/Xh7r///trqJfuz/twRcAQcgTgQKBsDWxkcku2ZmVrnDqist792BByB8kGgbA1s+Vyi/M+kadOmOdH3/EfxTzgCjkChCLiBLRRBg58fM2aMQa1cJUeg/iGQujSt+neJ/IxBYPfdd/dApN8KOyGwxx57mL8nGlBntpPW/sIRcAQcAUegKAj4DLYoMPogjoAj4AjkIuAGNhcT3+IIOAKOQFEQcANbFBh9EEfAEXAEchFwA5uLiW9xBBwBR6AoCLiBLQqMPogj4Ag4ArkIuIHNxcS3OAKOgCNQFATcwBYFRh/EEXAEHIFcBNzA5mLiWxwBR8ARKAoCbmCLAqMP4gg4Ao5ALgJuYHMx8S2OgCPgCBQFATewRYHRB3EEHAFHIBcBN7C5mPgWR8ARcASKgoAb2KLA6IM4Ao6AI5CLgBvYXEx8iyPgCDgCRUHADWxRYPRBHAFHwBHIRcANbC4mvsURcAQcgaIg4Aa2KDD6II6AI+AI5CLwf8MSxLPW1aKtAAAAAElFTkSuQmCC" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Then from naturality we get:\n", "\n", "![Screenshot%202021-05-04%20at%2019.10.04.png](attachment:Screenshot%202021-05-04%20at%2019.10.04.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2019.04.17.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Definition:** A compact closed category is a rigid symmetric monoidal category.\n", "\n", "**Lemma:** In a compact closed category, the following equations hold:\n", "![Screenshot%202021-05-04%20at%2019.04.17.png](attachment:Screenshot%202021-05-04%20at%2019.04.17.png)" ] }, { "attachments": { "Screenshot%202021-05-05%20at%2012.33.05.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Definition:** The transpose of a process is given by:\n", "![Screenshot%202021-05-05%20at%2012.33.05.png](attachment:Screenshot%202021-05-05%20at%2012.33.05.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2019.32.04.png": { "image/png": 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KqBHV1tU/a4xodmk1apfr5OrG6/noWxgoGHIaIYzeGz8zuWKabxZt7mShYslmuWL1xvqeTa1tvl2SfaCDo6O+k7yzgAvJFeu67PbRfcSj2/OOV/3Os97Hdh3ySfal+lHIvv4eAU6B9kE2wZYUyxCzUM0w2XCBCJbdNJGIyNWoH9Sf0Wux6DhivFCCxh6nxOikwuSWvVMpNPv5UmXStA/YpPsdjM84fKgysy1rOPt7LvNhhSP2eRFHD+fXFTw69u74eiFnkXKx3cnQkoOlZ041n+4tmznz6xxzucR57Qq7C+TK2KpD1cXwOdddN3eJeFmx3vFK1NW8a3UNnddHbnxpwjRz3JS8pXHbosXtTmBrTFvK3dT2Ax0H72V0Hrqf+SD7Ye6jw12HHx9+crg792nOs6yeQ73pfan9e5/H/RU1sHsw8kXMUNLLg8PHXpWPNLx+MPryzadx8JY4IfhOflJnynzab+bs+08flWeTPrV+/jWvuRD35fLXd4vsS5bfU340/Jxe4V51WMv+1bk9/8YIfeQO5GdUO/oQxhErjl3A3cRnEBxouGlGac/ThdOrMyAY2hnTmSyIDMRe0lFmWxYGlqes2Wwm7BB7M0cEpxDnEFcOtw73J55SXjPeb3xl/Gb8nwWOC2oIjgjtFeYXbhXxFlkVLRZTEusWDxBflTgmKSXZJuUoNSWdKiMiMySbu8Ngxze5KnlPBTqFNsVIJQGlfuU0FQWVcdU8NW21T+qlGuYai5rntey1fmnX6bjrYnVv6JH1ifp3DSIN+Q17jdKMlYynTUpMbeH3jtvmURZSFu8sy6w8rFmtn9sU2DrYkewG7U86eDsKO35wuuqc6GLsyuA67FbpHu1h4EnrOeh1Zmewt4L3yq77Pvm+Xn4SfkvkTv9jAb6BikGooMHgWkpKiFOodBg67E34rYji3fGRrlEaVN5oVPRszEBse1x9fFlC3p7UxPik0GT/vTv3uaU47XdItU+zP+CQ7nTQPWPnoYDM0Kzo7JSczNyCw2VHavIaj97L7ysYPfb5BKpQosir+OjJ+yUrp2RP+5WdOPP47Gq5wvmAipILPVWoaq2a+Nr6uo+XJC+H1Ndembum0rD/encjR1NYc+ctvtspLW9brdpa2uU7LnZK3b/60ODR8OOEbr6nvT2H+5yeiw6AwY9D74Y/vAZvRMZ3TdROoWcSP4JPFfPkr7pLaj+dV4s35n/rv7+NglEB4MQhADb+z3GoASD3IgBiewBgg3NPOzoAnNQBQsAUQIsdALLQ/nN/QHDiSQAkwAMkgRowg/PLMDinLAL1oAtMgDWIHVKGHKFo6ATUDL2Gcz5phAsiFVGPGEUyIA2Q8chLyCk4S/NClaJewZmYD/oC+hNGBZOKeYblwYZj23AkHAXXjufEx+L7CYqEIsIqDZnmKa06bTUdO10uPYI+if47QyzDEmMiE8SUTWQlVpDUSL3MISxYlgusxqxTbJnsUuy9HDGcHJytXP7cNNzXeDx4kbyX+DzhjKBPIE/QVohJ6LlwkYinqIDolNhF8WgJDUlIsksqX9oTXp3zsv07WuQq5QsU9ilSlByVNVT4VCHVMbUW9eMaIZraWvRaI9o1OjG6uno4vT79BoPrhk1Gt4xbTe6Zdpn1mA9ajFpOWy1Yr9ji7FjtRR3UHK2cyM7JLsWurW4zHiRPfa/IneXeAz4EX32/JHKz//dAtaCk4PYQQqhzWEX44m6zyLKouWitmJzY0XilhKN7FpJckx/s005pTbVMm0jPytDOBFl9OVcOn8oryDc7hjx+vzC/OKDE8JR0meBZkXKlCpvKqOrS2ieXQL3qVZsG9xvBTck3T9y+dqe/bamDt9PsQcyjs4+fda/1yPTtfH5k4O4QaZg8cml0dpx7Qm1Sb1r+Pf2HF7NHPu+Ya18w+9L5TWGxZGn5h/3PC8sLqxprKb/ubp4fW/NPhOdfAqgCE+AKQsA+cBzUgU4wCn5AJEgOsoEioKNQA/QSARAScJafhriKeAvn8VbIdGQbcgWljTqA6kazowPRjRg8xhvTiGXEhmGf4KRxebhFvBf+AUGWUESDpImiGad1pn1MZ0jXSq9FfwfOYh8x2jOOwnnqOvE4SZb0lDkCzjybWX3ZaNia2QM5WDkecu7hkuYa5y7iseXF8Xbw7ec3EMAIPBUsFPIVlhVeFekWLROLEjeW4JL4IvlY6rx0ioynrOYOCTl2ebz8qsKc4oTSC+XHKrdVL6qVqB/SoGp6ahlqS+ow6izqDuu16tcbXDVsMGoyvm3SZtpp9ti81+KF5RuraesFmxU7nD2rg5ijupO1s7/LXtcSt5vuwx5rXoI7Lbxjdp316fGDyCr+EQE1gVPBopSQkKuhy+GmEYW7Z6K0qHuj22JRcVbxRQlTiepJR5Kn9xmnVKfSp+05MA2fJ72ZFlkPc8xyu4845I3lpxzjPX63MLCY/mRzqf9pUtmDs3vLVc5/uXC1KrZGqw5zceDyhSvJ17yuqzTSN03cvH77wB2bNva74x01ndQHWo+wXYNPap7u7/Hq03kuMsA0+GjI+eXkq8TXzKPXxpzGVyeqJ92nGWa6PmTOWn5mnHuxcPZryKLKd8SPnuXS1aBfitvzjwQYQLt5AogDFXgFuIFwcBCcAbfBMLz/BSELKBaqgAYRNAgjeOd3IHFIe+QZ5BeUBaoKjUdT0W8wTvBut8EO4Mi4n/hCgjphkuYkrR7tCF0SPT99F0M8oyTjBNMZoh9JgvSd+SFLGWsSmye7HocUJzsXDTeCe5VnmXeVHwhg4TdQHmFZEW1RB7Eg8f0SJyVvwHn3vCzjDgU5V/l9ChWKPUorKhKq7moF6v2azFru2hU6c3ra+ocN3hgpGueYjJtpmRdafLGys75kS2sXZv/YUdIpx/mDq4VbrQfek+L10Ft010GfST9DcmUAMtA/6B5FNCQjdCbcKqI+kiUqgToWYxR7OZ49Yd+ej0lu8D5VSalK5Ug7ko46mJzxJdMj62r2eq7T4aojy0cd8y8fIxynnHhQJFWce3Ku1PXUnTLRM/nw2e9/vvuCZmVVNVNNYu3URcdLLfWiV/KuLjV4X3/QKNN0tHn+lv3ty3cIrYFtre3EjoB7jfdRD+welj6aeCzxhNJd+XS8h7PXvu9g//XnbwcIg3IvHIaoL48M17y6NzLwemp04c3qOPQWO4F5h5kEk8tTn6ZHZ56+b/5Q/jFzNuKT9WepOezcm/nmhawvHl8lvn751rKYtmT0HfO980fKT82fC8sXVjxWCauNa+RfdL+urbtvzH90oKLC5vUB0RoAgB5dX/8qCgC2AIC1/PX1lfL19bXzcLIxAsDdsK3vSZt3DSMAZ7k2UN+V9wL//paz9a3pH3nMv1uweRNtaoVvos0WvpXAfwEtFt65uwJTwAAAAFZlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA5KGAAcAAAASAAAARKACAAQAAAABAAAB9aADAAQAAAABAAAAagAAAABBU0NJSQAAAFNjcmVlbnNob3RnInRVAAAB1mlUWHRYTUw6Y29tLmFkb2JlLnhtcAAAAAAAPHg6eG1wbWV0YSB4bWxuczp4PSJhZG9iZTpuczptZXRhLyIgeDp4bXB0az0iWE1QIENvcmUgNS40LjAiPgogICA8cmRmOlJERiB4bWxuczpyZGY9Imh0dHA6Ly93d3cudzMub3JnLzE5OTkvMDIvMjItcmRmLXN5bnRheC1ucyMiPgogICAgICA8cmRmOkRlc2NyaXB0aW9uIHJkZjphYm91dD0iIgogICAgICAgICAgICB4bWxuczpleGlmPSJodHRwOi8vbnMuYWRvYmUuY29tL2V4aWYvMS4wLyI+CiAgICAgICAgIDxleGlmOlBpeGVsWERpbWVuc2lvbj41MDE8L2V4aWY6UGl4ZWxYRGltZW5zaW9uPgogICAgICAgICA8ZXhpZjpVc2VyQ29tbWVudD5TY3JlZW5zaG90PC9leGlmOlVzZXJDb21tZW50PgogICAgICAgICA8ZXhpZjpQaXhlbFlEaW1lbnNpb24+MTA2PC9leGlmOlBpeGVsWURpbWVuc2lvbj4KICAgICAgPC9yZGY6RGVzY3JpcHRpb24+CiAgIDwvcmRmOlJERj4KPC94OnhtcG1ldGE+Ct1+vUMAAB7MSURBVHgB7Z0J+FXDG8cny5/QgmSXSrKTJKGUtJCtkiQlSZR9y9r+WJ6nlIrwpHhKKkubUkhEhZQtS6JkL0m02c3//Q7z69dyf3fOueeeO/fc7/s8de/v3DlzZj7nnHln3nnnnVJaRFFIgARIgARIgATynsA2eV8DVoAESIAESIAESMAQoFLng0ACJEACJEACCSFApZ6QG8lqkAAJkAAJkACVOp8BEiABEiABEkgIASr1hNxIVoMESIAESIAEqNT5DJAACZAACZBAQghQqSfkRrIaJEACJEACJEClzmeABEiABEiABBJCgEo9ITeS1SABEiABEiABKnU+AyRAAiRAAiSQEAJU6gm5kawGCZAACZAACVCp8xkgARIgARIggYQQoFJPyI1kNUiABEiABEiASp3PAAmQAAmQAAkkhACVekJuJKtBAiRAAiRAAlTqfAZIgARIgARIICEEqNQTciNZDRIgARIgARKgUuczQAIkQAIkQAIJIUClnpAbyWqQAAmQAAmQQCRKff78+ap8+fLqvffeSxTRY445Rt19992JqhMrQwIksJGA1lpddNFFqkWLFhsPJuQb26+E3MiA1dguYPotki9fvlydffbZqkOHDgoPUZJkyJAhqmHDhuroo49WzZo1S1LVWBcSIAEh0LdvXzVlypTEDUhwc9l+FeYjXkp6qjps1f/880+j9NauXavefPNNtcMOO4TNytvzevbsqQYNGqTmzZunDj744FDlnDZtmurVq5eaM2eO2m67jPtRocqQq5M2bNhg6j1z5ky1aNEi9f3336vvvvtOrVixQu2yyy5q7733Nv/2228/deKJJ5rnqUqVKrkqLq9bQASef/55ddZZZ6kxY8ao888/P9Ka//333+qdd95ReO7xiefe/sOF7HO/zz77qJo1a6pTTz1V1ahRQ22zTSTG06K6RNF+NWnSxFgz2rVrV5Qvv/hLICOlftttt6nBgwebh7Z69er+1jKDkuHlrFevnlq9erVasGCBKl26dODc0Cm47rrr1O+//67+97//BT4/H09AQzZw4EA1fvx4hX7jCSecYCw5tjHba6+91Lp164oaumXLlqnXX39d4fOoo45SnTt3Vh07dgzFOx95sczxEoCF8bDDDjNm90cffTSyi3/77bemTRw5cqRauXKlsfLVrl1b7bvvvkWKHBeznVukx4Dogw8+UHgnLr74YnXNNdeY71EUKor2a9ddd1VdunThVGQUNySOPDBSDyOffPKJ3n777bWMQMOcnlfnfPrpp1pG2LpPnz6hyv3kk0/q3XffPdS5+XbS4sWLdcuWLXWpUqX06aefrseOHavXr1/vXI2FCxdq6SzqihUramkItTS4+q+//nI+nwlJwIWAzKNrUVb6p59+ckmeNo10+nW3bt30jjvuqKVTqmWwo6XjkPY8m0CsV1o6wfrwww/XO+20k7799tv1zz//bH/O6DPT9ksslFpM+RmVgSfHRwCjqFBy2mmn6T333FOL6T3U+fl20qWXXqp33nlnLT3rwEWXnriWefnA5+XTCb/99pvu0aOHFkuErl+/vn7rrbcyKj6eK3SiypQpo8U8qd99992M8uPJJGAJiEUIU466X79+9lBGn2K+N53QqlWrmk7sP//8Ezo/GVnrJ554QleuXFnLyF0/88wzofMqfmIm7VfTpk31hAkTimfH7x4TCKXUn376afNSDB061OOqRVu0L7/80igsMY85Z7x06VIt5mTTYz/33HO1mN/1+++/H1kP3LkgWU4INscdd5xp2NDARSnoRDVv3tywL6TnLUqGzGsjAVh9MJI+4IADNDqimYj4i+j27dubZxMd2kzzK16WX3/91YzWYQ3t1KlTxnkHbb/QVqEjDSubmN61rGzSMmWgP/zww+LF5HcPCQRW6uiFwhxTqVIlLY5yaas0adIkffzxx6dNl6sEqA/qIo5waYtw1VVXGbOyLOFLmxZsYLLHiEDmkc0nTHP4+/LLL097fr4k+Pzzz42Z/OSTTzYvfbbK/fDDDxc1ntm6BvNNPgGMgvEODhs2LKPKQqE3aNBAi4OnhiUuWzJ79mzTfjRu3FhD0WciQdovTKuCE9owdCwwVYG/8Q/KneIvgcBK/YUXXjA3tnv37k61wsgNc6O+CpQ6HtTXXnstbREx8kZa8QJNmxYJ8LKjh/vZZ59pmLDEcUaLN6z5dMrA80Tiwa5hckSDE+UoJVW1n3vuOdPAYL6SQgJhCNSpU8fMWa9ZsybM6eYcjPbPOeccM9qHJS7bsmTJEtOGtmrVSsM8H1aCtF/wNZgxY4axMl5yySUanQtx5tNz584Ne3meFxOBwEpdloAYxQaHKBdJklJHfcWLO3CjIEtnTAPgwitf0vzxxx8ao/Njjz1Wixd7bMV+/PHH9bbbbqvRuaSQQBACsnrFtF1t27YNctoWaeEQh5Hrxx9/vMVv2ToAhVq2bFntOphKVY4w7RcsrSNGjEiVJY97RiDQokgsN5o6dapZnlStWjUZtBaeXHjhhQprr8eNG+dceelpq6+//lqJInQ+x/eE4p2rxKtWTZw4UYkDYWzFxZIfLA+Uhtmsd4/twrxQ3hN44IEHTB0yWW8t1iJ13333KVnRog499NDYmBx55JEKy+QQ4VI6tKGvG7b9kmm20NfkifESCKTUZT5KiblaiXNIvKX06GoIUiEjRfXYY485l0rmwmARUWKidj7H54RYTz5gwAAlo2a1//77x17Ue+65R4l3sLrssstivzYvmJ8EECPiqaeeMmvFZeVOqEqsWrXKPHM33XSTkum0UHlkcpKY/JXMiyvxZFey3C1UVmHbL7RhlPwgEEipIwKTrD9WMreTH7XLQillGZ8SBxklc0tmpOpyCRtFDp2BfBeZT1Rdu3Y1HbszzjgjJ9URxx3TqXrppZdMcJucFIIXzSsCs2bNUuLJrc477zzTKQ9T+DvuuMPscdG7d+8wp0dyDjq0iNwpjmyh8gvbfiWh7QoFLA9Pclbq6KXK2mN1yCGHqAoVKuRhVaMrMpQ6BJ0cFxGvd5MsCWF0Ya3BNMy9997rUvWspZEgHaZzgYYWUbMoJFASAfuuih9ISclS/ibOrmr48OHGQpXL9xgRLfv3768eeughJcvUUpa3pB/CtF+5rHNJdeFvWxJwVuqYx4HpXbxHt8ylwI4g7CMEsdxdBEodFg47Ync5x8c0mEJAg4KROnr8uZZbb73VdDAwz0khgZIIWKUetv1CyGPEaM+Vdap43STmhQlxe//99xc/7Pw9TPtVKOGtnSF6nNBZqcvyBlONdC8FnMHEO1T9+OOPW602HMwkeM1Wf8vlwSBzRuINajZekGUeTkVGL1dCPzql9TkRYlRLeGCj1H0oJ2JlYyoIIygKCaQi8NVXXymMtBF/PYwPCNqG0aNHm/nsVNeI8zgGCJhbHzVqVCjn20Jrv2DJw7Shr4LBUpRO1M5KHZuZQNIpdcBDDxIvkASeKeKIUT6cSy644AIl8cCLjuf6CzYVgVjPWJfySOhS01PGTmPwbE8nUOjYkSzfBY5GdevWVRKsx5uqYC/sF198MbTjkDcVYUGyRsC17UpVAFgpoRgksmGqJLEfh28A2q6XX3458LULrf2C/4EPFpZUN0qWRho/CYkNkCpJoONOSh2eoxih2YehpCtAgUnENWNqxkuAHjIEHqd4ObDV4bPPPltSFrH+JrGVzfWwo1IQsSYsl9F6+fLlVbly5YJk72XayZMne9WwARLmB/HMTZ8+3UtmLFTuCUi4U1MI+84GLRGeewmwFOvSzXRlRHvSsGFDhbKFEcuikNqvMJzy8Rwnpf7RRx8p7J2Ofa5h+kkn2DoTe2fD7IylT1jK9corr5htDsM+hOmuGfZ360WKjohEmXLOxq7Tt6OAkk7cbbfdjNdsSWl8/w0WCYlIpWTnNa+KCk94dBjhCU8hga0RkKiO5vBBBx20tZ/THsOz5dtzj0LD8hn2uS+09ivtTU5QAielbl+KIPNRSIsROdZTwqywzz77eDVCxz3EHsGYb4NgXiPd1IJJ+N9/loWLByqcyjD/m8+CHj32Qpe4/95VA/vdu4w4vCs4CxQLgTDtly0YVnp888036pRTTrGHvPlEmdDZxt7sQaXQ2q+gfPI5vZNSt4rPPgiuFcY8huwjbhSm7Mfrelos6a6//nolm4QoCXNqrte6dWuFuY1atWoZL/90hbAsXJU6ArXks8AiATY+Chx/MM0TxNLiYz1YpugJYC5cdvozGdt3NshV8Nxj+syObIOcm+20WNaJaI4u1sLNy2JZuLRfiGJXo0aNzbPg354ScFLqmbwUdilEixYtvEGAqEpw5kOYR9nIxZTriiuuUHC6ghleNilJq9iDvBS4gMSK9qb+YQqCKRiEqvRR0LhB4PdBIYHiBJYvX27eZUwF7rHHHsV/cvqO5/6II45wmnZ0yjDCRAgIgzYMg5GgEqT9yve2KyibfE/vpNS/++47U0/7IASpNOJ0+7acC+vGEeoRL0PxsmGJCGI6Y6oA3volCbz7t9lmGzO9UAgjxC+++MJ0dkpikqvfsLIAUxyY86eQQHECtu2SLVJDKWafn3vUEwOQMM99obVfxZ+JpH8PpNTDzAsfcMAB3o1SsTFCv379tnpv27RpY4LKpAsUAwctOMBBsFlL0gUjHsyp+yroiKGMFBIoTsAq9TBtF/JJ6nNfaO1X8Wci6d+dlPoPP/xgOBQf1SYdjEv9LI+kj9SxpBEBOHw2w2HeM+wmFy73mmnyk0CmbReeqaQ+94XSfsHZ0cV3IM4nHEGzxo8fv9VLDhs2THXq1Gmrv7kcdFLqNtqajWHuknEhpLE8LJ+k1tlGO/I5/jPKZsuZ1PvAegUnYN9N+64GzQHPVFKfe8vEMgrKJl/SIxrg4sWLvSouYie0bNlSYStpKzZAW+fOndWHH35oDwf+3M7lDIzUIPYhcDmnENJYHrnYUhX72q9du9YZMxomxIx2iTOweaZY7ue7hKmX73Vi+TInkGnb5fuzn8lzn6v2C6NmhJwOwharlMIup7XXQehyXzYjQycDq3YwFWzL17FjRxOgDTER7F4FYd4AKvUw1P47BzsmQeLu6eIhmDhxYmCljmAVtsz/VYEfJJBoApkq9STDsW1B3O0XHJTRflll5sIYTslhlLrd9Aadn/bt22ekLF3K6ZoG9cFKKwRqgyUBMmXKFBMlMBOFjnzSKnXEcrdbW9qeHU6kbLRcxP1S4AHFvAuFBEigZALWisa2a0tOlknc7RdGonFE6IOJG6uc4CQJx8Bp06apoUOHerMhFe4ILBbwB4LpHat4sI9FppJ2Tr340i6si6RsJGB5BOlxbjyb30iABLJNwLZf9l3N9vXyKX/LJInt16xZs9QJJ5xgphsRl+SQQw4xcQqwu919993nzW2Cs2KTJk1MeTCXjhF8ppJ2pI7gMbgQXg7b6830okk53/JIt/wt6vriJbztttvMLk2ueWNOHZGhfHb6ca0L05GAKwFrYrbvqut5hZDOMom7/YLCDbr9NqKTuu60hhH6qaeeato67GKHjcQgCxcuVMcdd5wZvePvG2+8ER85F3Q4YHqPynqRVqmjxngx1q9fT6W+2e23L0XcihLm98MOOyzQnDo6Z3G/vJvh4p8kEDsBKvXUyHPVflWsWNFEwktdsi1/CRJnAObsdu3aqcGDB6uyZcsWKXUEqIKTXrdu3byKjolIpv37948sFG/BK/VMvEftS2HnprZ8FLN3BE4fFBIggZIJUKmn5pOr9guhbfEvW1K5cmWVaq8NWJ2hQH2SqAdbTgZ8+2KEcagAROto5xNIWxZbNju/ZI+7fNqXIu6RukvZmIYESOBfKyM4hGm7ks6P7Vcy73AgpW4fgiAosIsQTPe+yrp160zRbHSlIOW0PMqVKxfkNKYlARKIiYAdkNh3NabL5sVlLBO2X3lxu5wL6aTUbczv1atXO2dsE2KxP4Kk2AfIHvflEwEJIGGCElge2BwhabJixYoSN7UJs4dzNhlh6aX1dM7mdZh3fhHIpO1CTX18rkp69xDWdsOGDU43KcntlxOAhCZyUuqVKlUy1Q+zcQl2R4LYPdnNHx79B8cJzGkEccRA8dEZgEkPZns4fiRNjjnmGNPRmTt37iZVw77leB4wb+WTvPTSS+rhhx/2qUgsiwcEMmm7UHx4TMPhyhfB3unYvAiBpDYPi4y5Ymwve8kll6QtbtLbr7QAEpwg60odDyAW1S9atMhLjJ9++qmqUqVKYM9w28GBR2WY+XgvYRQrFLagRY+/bt26asaMGeYXbPGIvaW//fZb9cgjjxRLnfuvWOaX9I11ck85/0qAQQX8ejAqDToNaC0/dqc3H2pfs2ZNBW9pLNNChDVbRqy/vvnmm43Cf/DBB9MWNentV1oACU7gpNSxfSrEPghBeMC7/Mgjj1TvvfdekNNiS4s1jQjVF1QsiySa3sGiQYMG6pNPPjFrPdGIQK644grj9Dhz5sxNNiIwP+bwvyeeeKLo6kuWLCn6zi8kgEhi1gRv31lXKn369DFJ//zzT686jKNGjTJxKmBlHDdunJnehCKHRzn2f3eZSrQsktp+ud7jJKZzUuqZmrBq166tNjfj+gIT5ULkoaBiXwqsF0+qwMT+yiuvFPlDrFy50iwVqVevnjdVhqMjOhuwBmEtfqNGjbwpGwviB4Ew7ResUQjWhOcKI33fniuU7cwzz1QffPCB+vzzzxWc3TBwQlldpBDaLxcOSUzj9ATYNYXoGYYRjPpmz56t7OYKYfLIxjlwOMHmAvXr1w+cvfURqFGjRuBz8+kEdMhOO+00U2QoeTtq96EOmB5ANCaYVY8++miFzgZGKpgyoJCAJRC0/cIe7JhmwnJXdAhOPvlkNW/ePIVwoz7Js88+azZFgRPyQw89ZDq1ruUrlPbLlUeS0jkpdcxLwQSP3iu8ooMKQvbBixRmW58EofkwJx5GMb/zzjumKmHO9YmBS1muvvpqk+yUU05xSR5LGpjZ999/f/NM9urVy4xUEAIS28uiAwllb5crxlIgXsRbAieddJIpG5zM0snbb79tfGx++eUX4zcC60/z5s2NNQ+hTevUqWPasnT5xPG7DeGNa7Vp0ybQJQup/QoEJoeJo4rB76TUUU/7YmBXmaACE1bjxo3VU089FfTUrKbHSwol4GqysoWBcwp67vAXgJd40gV7GUN8GgFjZALvXzxTPXv2LLoFEyZMUH379lXLli2LZMejooz5JW8JBGm74EGOYFKIGd6pU6eiOr/xxhvq2muvVVCG77//ftHxXH+BhSpoRLJCa7/AB4NKX8WWLeh9TFUfZ6UOExTkrbfeSpVXicdhtn3mmWcUesA+CMy0sByEMSd/9NFHxnEGDoCILZx0KVOmjKmiVe4+1BeNL+IftGrVaovi3HnnncYPoEWLFlv8xgOFRwBe4ljqheVp6dZww/Fs1apVxlF0c1LYmxtTiPBA90Vat26tatWqFag4hdZ+YVDps9UOZcMAEYHaohBnpR6kt7u1gmFEDGcO7Gfrg2D7PShlW68gZUKvHeK6a1CQvJmWBEggegJ4zzFHPn/+/Ogzz7McC639QocOfhK+Cqa0d91118AWl1T1cVbqUIC77767wpyTNRekynRrxzH/c8stt6h+/fopeFHnUhYvXqyGDRumevToEaoYhfZShILEk0jAIwJw1oX4ugonTlSF1n5ZfzAsTfRR4IBul41HUT5npY555wsvvNCYMV588cVQ18bSI6wZzeU+tnBG6NKlixmhw3oQVNDbnz59usL2fnCaoZAACfhPAGZqzFmOHz/e/8JmsYSF2H5h+gUDUUTD9FEQDwRljEqclTouaMMPjhkzJtT1EQji0UcfVYhWliunOcyLwS8AEdHCbLuKcKTLly9XZ599dmTmklAweRIJkIAzAaxywXQZLI1Y112oUojtF6KaIpS39fj37d6jXFE6XAdS6li+hYtPnDgx9FaGGN3CW/myyy5TcNiIU1577TUzBTBkyBBVrVq1UJdGNCdI165dQ53Pk0iABHJDoGPHjubCYQcluSl1tFct1PYLemfOnDnRwowgNzj7YjVFlFbfQEoddcBoHd56kydPDl2lO+64Q2Ht+llnnRVq3XuYC2MevWXLlqYzYS0OQfPBDUCHBuuhEZSFQgIkkD8EMFLHiA2WwkKUQm6/4FMBK4Vv8uqrrypYsMNENU1Vl8BKvW3btgp7jw8fPjxVnmmPY34e8brhlQjlbkMWpj0xZAJEjWvYsKFRxIMGDQqZizJL8rAkBpsnUEiABPKLABrPDh06mM2lCtFhDkuKC7X9atasmULAqritw+neEAyOoZt23HHHdEndfxfHscAi5nMtV9Bizg58bvETfvrpJy0BTbTMd+lp06YV/ymy79J50LKWXItTnJYHOnS+4mihDz/8cC1eilq2XA2dTz6eKGtztQR70bJdo7fFnzp1qpbASN6WjwXzg4CsQdeyfEjLYMKpQBKgSkt8dae0uUgkG1Jpcf5Le+lCbr8sHAnUo7t3727/zPkn2lVZUaYfe+yxSMuC2MGBRWJta9ndR0us7cDnbn6CxC3WN9xwg5bRu5ZAMFq2Odw8Sai/xdNRy4YHWnrn+q677tJ4qDMRcfAzHRmJt5xJNjyXBEggxwTEWda8yxJ8Ksclie/ybL+0loBVWkKea4lEGR/4Eq4kvh1aAs5oCchWQqrgP4VS6rjMyJEjzYsh+/oGv+pWzhAnBi2OeKaSsp5dS7CAraRKf0g2KtCyZE3Lungtscoj6WVjhI9OjIS6TV8ApiABEvCaABr16tWra3FO8rqcURWO7de/JGGlkehyesSIEVGhDZ2PhOrVsBxceeWVofNIdWJopY5CibOYlt2MIjNHyxpKPXr0aPPCQSnLXIOWyG9a5sRTjrTxgsIEhdG4RI3S2267rZZwpvq5555LVefAx2XDENNJWLRoUeBzeQIJkIB/BDBdgylETM8lXdh+bbzDEkLajNbF2XvjwRx8e/zxx3Xp0qW1+JNFfvXQSh0lWbp0qZkTkF28Ii0YlPvrr79uzPKy3ad5+aCsJXCNUdiyFaiWpXVaPFmN2R4vp+xrrsWrXksYSI0OR1SCeVoJWqEHDBgQVZbMhwRIwAMC119/vfG3QTuWVGH7temdlRUAWnZ31LI5z6Y/xPiXhIXV4iSue/funZWrlkKu7m51W6acMWOGOv30081SL3gYZkOw4xb2/8X+5/i3evVqVaFCBROdDhHqDjzwQCXm8cgvvWbNGrMu//jjj1djx46NPH9mSAIkkDsCiK6G3SPF8VUhhkVUu2TlrkabXpnt16Y87F+ICCr+Vgpbbzdt2tQejuUT6hbXFt8xEwQN4dMjlyi6CnBAQM8DPZAkiYTFNRaBXJtqksSUdSEBnwhgRYcMCjRW9CRN2H6lvqM33XSTsTJLdMHUibLwi+w3omXXSy2hYbOQ+79ZZjxSt70MhH0Vs7jabbfd7KG8/5T5fdWoUSMTsCLvK8MKkAAJbJUAYoLDEoj1wkkStl+p7yZiwWPEDCvw7NmzjeU3depofhHncoWohth/AGHGsyWRKfVsFZD5kgAJkAAJkEDUBDA9Ub9+fYXd255//nklc+1RX6IoP+wKitDiAwcOzHrwssAR5YpKyS8kQAIkQAIkkKcEJCiZCR2Lvcxr1qypJk2aFHlNEJr30ksvNQode47EEY2USj3y28gMSYAESIAE8oGARHRTcPaG4sXeIC1atFCyGiLjosvstsL0h6zKUojvjn/YejwOoVKPgzKvQQIkQAIk4CUBeKDfc889at68eWrlypXq0EMPNSPrMModKyomTJhgRv7YiRSbh0mYYSUxVGKrO+fUY0PNC5EACZAACfhMACNsCUykZA25WrBggcJ2402aNDFOlFWrVlV77bVX0eYrSIvl1VhmLfFRlERXNaN+a3K/9dZblYSljb26VOqxI+cFSYAESIAEfCeA3T2h4OFEh73Y4VBXqlQphTl4CTerJJS5kr1LTDWg7BGvBdv7YsVUuXLlclY9KvWcoeeFSYAESIAE8oGAhCNXy5cvN/8wMpfYJUp2FzUjdwRAw1JuKHwfhErdh7vAMpAACZAACZBABAToKBcBRGZBAiRAAiRAAj4QoFL34S6wDCRAAiRAAiQQAQEq9QggMgsSIAESIAES8IEAlboPd4FlIAESIAESIIEICFCpRwCRWZAACZAACZCADwSo1H24CywDCZAACZAACURAgEo9AojMggRIgARIgAR8IECl7sNdYBlIgARIgARIIAICVOoRQGQWJEACJEACJOADASp1H+4Cy0ACJEACJEACERCgUo8AIrMgARIgARIgAR8IUKn7cBdYBhIgARIgARKIgACVegQQmQUJkAAJkAAJ+ECASt2Hu8AykAAJkAAJkEAEBKjUI4DILEiABEiABEjABwJU6j7cBZaBBEiABEiABCIgQKUeAURmQQIkQAIkQAI+EKBS9+EusAwkQAIkQAIkEAEBKvUIIDILEiABEiABEvCBwP8BCi7xn2i7qwUAAAAASUVORK5CYII=" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Definition:** A $\\dagger$ compact closed category is a compact closed category with a dagger, such that swaps are unitaries and![Screenshot%202021-05-04%20at%2019.32.04.png](attachment:Screenshot%202021-05-04%20at%2019.32.04.png)" ] }, { "attachments": { "Screenshot%202021-05-05%20at%2012.33.44.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "In a $\\dagger$ compact closed category, we get a $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$ action on processes:\n", "![Screenshot%202021-05-05%20at%2012.33.44.png](attachment:Screenshot%202021-05-05%20at%2012.33.44.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2022.01.23.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Compact closed categories allow to formulate the notion of **entanglement** in an abstract setting.\n", "\n", "**Definition:** A state $w : 1 \\to A \\otimes B$ is separable when it can be written as a tensor $w = v \\otimes v'$ for some $v : 1 \\to A$ and $v' 1 \\to B$.\n", "\n", "**Definition:** A state $w : 1 \\to A \\otimes B$ is entangled if it is not separable.\n", "\n", "**Lemma:** The cup of a non-trivial system is entangled.\n", "\n", "_Proof:_ Suppose the cup is separable, then the identity factors through the unit.\n", "\n", "![Screenshot%202021-05-04%20at%2022.01.23.png](attachment:Screenshot%202021-05-04%20at%2022.01.23.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2023.19.35.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Lemma (Teleportation):**\n", "![Screenshot%202021-05-04%20at%2023.19.35.png](attachment:Screenshot%202021-05-04%20at%2023.19.35.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2023.20.39.png": { "image/png": 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" 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "We can also formulate an abstract version of the **no-deleting** and **no-cloning** theorem.\n", "\n", "**Definition:** Deleting is a natural transformation $e_A : A \\to 1$ with $e_1 = 1$.\n", "\n", "**Lemma:** A monoidal category has deleting if and only if $1$ is terminal.\n", "\n", "**Theorem:** If a compact closed category has deleting, then it is a preorder.\n", "\n", "_Proof:_ Take two parallel arrows $f, g : A \\to B$, then their coname $\\hat f, \\hat g : A \\otimes B^\\star \\to 1$ are equal, hence $f = g$.\n", "\n", "**Definition:** Copying is an commutative, associative natural transformation $d_A : A \\to A \\otimes A$ such that:\n", "\n", "![Screenshot%202021-05-04%20at%2022.14.19.png](attachment:Screenshot%202021-05-04%20at%2022.14.19.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2022.14.23.png": { "image/png": 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" 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Lemma:** If a braided monoidal category has copying, then:\n", "\n", "![Screenshot%202021-05-04%20at%2022.24.57.png](attachment:Screenshot%202021-05-04%20at%2022.24.57.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2022.27.41.png": { "image/png": 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" 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Theorem:** If a compact closed category has copying, then:![Screenshot%202021-05-04%20at%2022.25.26.png](attachment:Screenshot%202021-05-04%20at%2022.25.26.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2022.30.17.png": { "image/png": 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" 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### Special commutative Frobenius algebras\n", "\n", "**Definition:** A Frobenius algebra is a pair of a monoid and comonoid such that:\n", "![Screenshot%202021-05-04%20at%2022.37.18.png](attachment:Screenshot%202021-05-04%20at%2022.37.18.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2022.37.28.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Definition:** A Frobenius algebra is dagger when the dagger of multiplication is comultiplication, and the dagger of unit is counit.\n", "\n", "**Definition:** A $\\dagger$ Frobenius algebra is commutative when its monoid is commutative.\n", "\n", "**Definition:** A $\\dagger$ Frobenius algebra is special when ![Screenshot%202021-05-04%20at%2022.37.28.png](attachment:Screenshot%202021-05-04%20at%2022.37.28.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2022.46.07.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Lemma:** Frobenius algebras are self-adjoint.\n", "\n", "_Proof:_ Define cups and caps\n", "![Screenshot%202021-05-04%20at%2022.46.07.png](attachment:Screenshot%202021-05-04%20at%2022.46.07.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2022.46.04.png": { "image/png": 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" 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Lemma:** Homomorphisms of Frobenius algebras are isomorphisms, with inverse given by\n", "\n", "![Screenshot%202021-05-04%20at%2022.49.22.png](attachment:Screenshot%202021-05-04%20at%2022.49.22.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2022.49.59.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "_Proof:_ Suppose $f$ is a homomorphism of Frobenius algebras.\n", "![Screenshot%202021-05-04%20at%2022.49.59.png](attachment:Screenshot%202021-05-04%20at%2022.49.59.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2022.51.16.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Theorem (Spider Fusion):** Every connected diagram $d : A^{\\otimes n} \\to A^{\\otimes m}$ generated by the co/monoid of a Frobenius algebra is equal to a spider-shaped diagram![Screenshot%202021-05-04%20at%2022.51.16.png](attachment:Screenshot%202021-05-04%20at%2022.51.16.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2022.53.38.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "_Proof:_ By induction, we move all the black comonoid below the white monoid.\n", "\n", "![Screenshot%202021-05-04%20at%2022.53.38.png](attachment:Screenshot%202021-05-04%20at%2022.53.38.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2023.09.13.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Theorem (Artin–Wedderburn):** in $\\mathbf{FHilb}$, $\\dagger$ special commutative Frobenius algebras are in one-to-one correspondance with orthonormal bases.\n", "\n", "_Proof:_ $C^\\star$ algebra magic.\n", "\n", "The correspondance sends a $\\dagger$ SCFA to the basis of copyable states:\n", "![Screenshot%202021-05-04%20at%2023.09.13.png](attachment:Screenshot%202021-05-04%20at%2023.09.13.png)" ] }, { "attachments": { "Screenshot%202021-05-04%20at%2023.11.05.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "It sends a basis to the Frobenius algebra given by:\n", "![Screenshot%202021-05-04%20at%2023.11.05.png](attachment:Screenshot%202021-05-04%20at%2023.11.05.png)" ] }, { "attachments": { "Screenshot%202021-05-05%20at%2003.00.05.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Frobenius algebras not only characterise bases in $\\mathbf{Hilb}$, they also allow us to formulate an abstract notion of **phases**.\n", "\n", "**Definition:** Given a $\\dagger$SCFA, a phase is a state $a : 1 \\to A$ such that:\n", "\n", "![Screenshot%202021-05-05%20at%2003.00.05.png](attachment:Screenshot%202021-05-05%20at%2003.00.05.png)" ] }, { "attachments": { "Screenshot%202021-05-05%20at%2003.00.14.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "It defines a phase shift map, a.k.a. diagonal unitary matrices:\n", "![Screenshot%202021-05-05%20at%2003.00.14.png](attachment:Screenshot%202021-05-05%20at%2003.00.14.png)" ] }, { "attachments": { "Screenshot%202021-05-05%20at%2003.00.26.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Lemma:** Phases form a group.\n", "\n", "![Screenshot%202021-05-05%20at%2003.00.26.png](attachment:Screenshot%202021-05-05%20at%2003.00.26.png)" ] }, { "attachments": { "Screenshot%202021-05-05%20at%2003.06.15.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "_Proof:_\n", "Associativity and unit follow from that of Frobenius algebras. Define the inverse as follows.\n", "![Screenshot%202021-05-05%20at%2003.06.15.png](attachment:Screenshot%202021-05-05%20at%2003.06.15.png)" ] }, { "attachments": { "Screenshot%202021-05-05%20at%2003.06.17.png": { "image/png": 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