The Logic of Quantum Mechanics - take II - Perimeter Institute

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— challenge — What can we do with stuff of this kind: Given that: • GHZ/W-calculus encodes rational arithmetic • We have automation support
Posters on this line of work: • Aleks Kissinger: Synthesising physical theories. • Raymond Lal: Causal structure in categorical quantum mechanics. • Johan Paulsson: Towards a diagrammatic representation of classical data. Also from the Oxford gang: • Shane Mansfield: Hardy’s non-locality paradox and other possibilistic non-locality conditions. Want to learn this kind of category theory? Try: • BC & E. O. Paquette (2010) Categories for the practicing physicist. In: New Structures for Physics. BC (Ed.), Springer. arXiv:0905.3010
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The Logic of Quantum Mechanics - ta
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— genesis — [von Neumann 1932]
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— the mathematics of it — Hilbe
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— the physics of it —
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— the physics of it — von Neuma
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— the physics of it — von Neuma
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— the game plan — Task 0. Solve
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— the game plan — Task 0. Solve
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Outcome 1a: “Sheer ratio of resul
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Outcome 2a:
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— the logic of it —
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— the logic of it — WHAT IS “
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— the data of tensor logic — Bo
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— the data of tensor logic — Bo
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— the connectives of tensor logic
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— merely a new notation? —
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— merely a new notation? — (g
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— merely a new notation? — (g
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— topological connectedness as a
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— topological connectedness as a
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A MINIMAL LANGUAGE FOR QUANTUM REAS
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— graphical notation for states a
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— adjoint — f † : B → A A f
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= = — asserting (pure) entangleme
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— quantum-like — =
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classical data flow? f f f f =
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classical data flow? f f =
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— symbolically: dagger compact ca
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— the from-words-to-a-sentence pr
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— the from-words-to-a-sentence pr
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= — the from-words-to-a-sentence
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— grammar as pregroups - Lambek
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— from gammer to meaning — For
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— −−−→ Alice ⊗ −−
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— −−−→ Alice ⊗ −−
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— experiment: word disambiguation
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— analogy: “non-local” info-f
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THE EXTENDED LANGUAGE: BASES AND CO
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— commutative Frobenius algebras
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— commutative Frobenius algebras
Page 113 and 114: commutative monoid cocommutative co
Page 115 and 116: commutative monoid cocommutative co
Page 117 and 118: — commutative Frobenius algebras
Page 119 and 120: — bases in tensor logic — The n
Page 121 and 122: such that, for k > 0: — spiders
Page 123 and 124: such that, for k > 0: — spiders
Page 125 and 126: — complementary bases —
Page 127 and 128: — quantum gates — Z-spin: δ Z
Page 129 and 130: — quantum gates — ⎛ ⎜ ⎝ 1
Page 131 and 132: — quantum gates —
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Page 135 and 136: — classical communication and con
Page 141 and 142: qubit 1 the leftmost, and qubit 4 i
Page 143 and 144: — automated theory exploration
Page 145 and 146: Defn. Special CFA (SCFA): =
Page 147 and 148: = = Defn. Special CFA (SCFA): Lem.
Page 149 and 150: — C(F)As ←→ tripartite states
Page 151 and 152: = = Theorem. If a CFA on C 2 is spe
Page 153 and 154: — W algebra — ( 1 0 0 0 ) ( 1 0
Page 155 and 156: — W “exploding spiders” — D
Page 157 and 158: — GHZ-W interaction —
Page 159 and 160: Informatics information flow vs no
Page 161 and 162: ( ) (( ) ( )) 1 0 0 0 1 1 ⊗ 0 0 0
Page 163: ( ) (( ) ( )) ( ) 1 0 0 0 1 1 1 ⊗
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