The Logic of Quantum Mechanics - take II - Perimeter Institute

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— the logic of it — WHAT IS “LOGIC”? Pragmatic option 1: Logic is structure in language. “Alice and Bob ate everything or nothing, then got sick.” connectives (∧, ∨) : and, or negation (¬) : not (cf. nothing = not something) entailment (⇒) : then quantifiers (∀, ∃) : every(thing), some(thing) constants (a, b) : thing variable (x) : Alice, Bob predicates (P (x), R(x, y)) : eating, getting sick truth valuation (0, 1) : true, false (∀z : Eat(a, z) ∧ Eat(b, z)) ∧ ¬(∃z : Eat(a, z) ∧ Eat(b, z)) ⇒ Sick(a), Sick(b)
— the logic of it — WHAT IS “LOGIC”? Pragmatic option 1: Logic is structure in language. Pragmatic option 2: Logic lets machines reason.
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 and 18: — the physics of it — von Neuma
Page 19 and 20: — 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 37: — 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
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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
Page 109 and 110:
— commutative Frobenius algebras
Page 111 and 112:
Page 113 and 114:
commutative monoid cocommutative co
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commutative monoid cocommutative co
Page 117 and 118:
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:
Page 141 and 142:
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:
Posters on this line of work: • A
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