The Logic of Quantum Mechanics - take II - Perimeter Institute

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— commutative Frobenius algebras — A commutative monoid is vect. space V & lin. map µ : V ⊗ V → V which is commutative, associative and unital i.e µ◦(µ⊗1 V ) = µ◦(1 V ⊗µ) µ = µ◦σ µ◦(1 V ⊗e) = 1 V A cocomutative comonoid is vect. space V & lin. map δ : V → V ⊗ V which is cocommutative, coassociative and counital i.e (δ⊗1 V )◦δ = (1 V ⊗δ)◦δ δ = σ◦δ (1 V ⊗e ′ )◦δ = 1 V
commutative monoid cocommutative comonoid ˆ+ Z2 :: { |00〉, |11〉 ↦→ |0〉 |01〉, |10〉 ↦→ |1〉 ˆ+ † Z 2 :: { |0〉 ↦→ |00〉, |11〉 |1〉 ↦→ |01〉, |10〉 ˆ× B :: · · · ˆ× † B :: · · · δ † Z :: { |00〉 ↦→ |0〉 |11〉 ↦→ |1〉 δ † X :: { | + +〉 ↦→ |+〉 | − −〉 ↦→ |−〉 δ Z :: δ X :: { |0〉 ↦→ |00〉 |1〉 ↦→ |11〉 { |+〉 ↦→ | + +〉 |−〉 ↦→ | − −〉 δ † Y :: · · · δ Y :: · · ·
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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
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 and 94: = — the from-words-to-a-sentence
Page 95 and 96: — grammar as pregroups - Lambek
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: 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
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 and 164: ( ) (( ) ( )) ( ) 1 0 0 0 1 1 1 ⊗
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Posters on this line of work: • A
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