The Logic of Quantum Mechanics - take II - Perimeter Institute

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— grammar as pregroups – Lambek ’99 — I ηl → A ⊗ A l A l ⊗ A ɛl → I Al A A A l Ar A A A A I ηr → A r ⊗ A A ⊗ A r ɛ r → I A A A r A A = = = A A l A l A A r A r = A l A l A r A r
— grammar as pregroups – Lambek ’99 — For noun type “n”, verb type is “ −1 n · s · n −1 ”, so: n · −1 n · s · n −1 · n = s
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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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Page 43 and 44: — 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 73 and 74: — adjoint — f † : B → A A f
Page 75 and 76: = = — asserting (pure) entangleme
Page 77 and 78: — quantum-like — =
Page 79 and 80: classical data flow? f f f f =
Page 81 and 82: classical data flow? f f =
Page 83 and 84: — symbolically: dagger compact ca
Page 89 and 90: — the from-words-to-a-sentence pr
Page 91 and 92: — the from-words-to-a-sentence pr
Page 93: = — the from-words-to-a-sentence
Page 97 and 98: — from gammer to meaning — For
Page 99 and 100: — −−−→ Alice ⊗ −−
Page 101 and 102: — −−−→ Alice ⊗ −−
Page 103 and 104: — experiment: word disambiguation
Page 105 and 106: — analogy: “non-local” info-f
Page 107 and 108: THE EXTENDED LANGUAGE: BASES AND CO
Page 109 and 110: — commutative Frobenius algebras
Page 113 and 114: commutative monoid cocommutative co
Page 115 and 116: commutative monoid cocommutative co
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 —
Page 133 and 134: — quantum gates —
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
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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 ⊗
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Posters on this line of work: • A
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