The Logic of Quantum Mechanics - take II - Perimeter Institute

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— the physics of it — von Neumann crafted Birkhoff-von Neumann Quantum ‘Logic’ to capture the concept of superposition. Schrödinger (1935): the stuff which is the true soul of quantum theory is how quantum systems compose. Quantum Computer Scientists: Schrödinger is right!
— the physics of it — von Neumann crafted Birkhoff-von Neumann Quantum ‘Logic’ to capture the concept of superposition. Schrödinger (1935): the stuff which is the true soul of quantum theory is how quantum systems compose. Quantum Computer Scientists: Schrödinger is right! 75 years later Birkhoff-von Neumann quantum ‘logicians’ still fail to elegantly capture composition of quantum systems, ... nor much else neiter, ...
Page 1 and 2: The Logic of Quantum Mechanics - ta
Page 3 and 4: — genesis — [von Neumann 1932]
Page 9 and 10: — the mathematics of it — Hilbe
Page 15 and 16: — the physics of it —
Page 17: — the physics of it — von Neuma
Page 21 and 22: — the game plan — Task 0. Solve
Page 23 and 24: — the game plan — Task 0. Solve
Page 25 and 26: Outcome 1a: “Sheer ratio of resul
Page 31 and 32: Outcome 2a:
Page 33 and 34: — the logic of it —
Page 35 and 36: — the logic of it — WHAT IS “
Page 45 and 46: — the data of tensor logic — Bo
Page 47 and 48: — the data of tensor logic — Bo
Page 49 and 50: — the connectives of tensor logic
Page 51 and 52: — merely a new notation? —
Page 53 and 54: — merely a new notation? — (g
Page 55 and 56: — merely a new notation? — (g
Page 57 and 58: — topological connectedness as a
Page 59 and 60: — topological connectedness as a
Page 61 and 62: A MINIMAL LANGUAGE FOR QUANTUM REAS
Page 63 and 64: — graphical notation for states a
Page 69 and 70:
— graphical notation for states a
Page 71 and 72:
— graphical notation for states a
Page 73 and 74:
— 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
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
— 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
Page 111 and 112:
Page 113 and 114:
commutative monoid cocommutative co
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commutative monoid cocommutative co
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Page 119 and 120:
— bases in tensor logic — The n
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such that, for k > 0: — spiders
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such that, for k > 0: — spiders
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— complementary bases —
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— quantum gates — Z-spin: δ Z
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— quantum gates — ⎛ ⎜ ⎝ 1
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— quantum gates —
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— quantum gates —
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— classical communication and con
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Page 139 and 140:
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qubit 1 the leftmost, and qubit 4 i
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— automated theory exploration
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Defn. Special CFA (SCFA): =
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= = Defn. Special CFA (SCFA): Lem.
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— C(F)As ←→ tripartite states
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= = Theorem. If a CFA on C 2 is spe
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— W algebra — ( 1 0 0 0 ) ( 1 0
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— W “exploding spiders” — D
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— GHZ-W interaction —
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Informatics information flow vs no
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( ) (( ) ( )) 1 0 0 0 1 1 ⊗ 0 0 0
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( ) (( ) ( )) ( ) 1 0 0 0 1 1 1 ⊗
Page 165:
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