Manuscript En02-A@1 · En02-A-v1.tex · section · bb1319d5

Kinematics and destructive components

Finite operational strategies and explicit requirements › Kinematics and destructive components · lines 293–325

For a finite set $L$ of live qubit names, let

H_{L} = q \in L ⨂ C^{2} .

An ordering of $L$ is used only to write coordinates. Global states are unit rays. For $S \subseteq L$ and $κ \in {0, 1}^{S}$ , define

M^{S}_{κ} = ⟨ κ ∣_{S} \otimes I_{L ∖ S}, b^{S}_{ψ} (κ) = M^{S}_{κ} ψ^{2} .

On a positive Born branch the destructive projective residual is

ψ^{S}_{L, κ} = \frac{M ^{S} _{κ} ψ}{b ^{S} _{ψ} ( κ )} .

The measured factors are removed, not retained.

For finite laws,

d_{TV} (p, q) = \frac{1}{2} x \sum ∣ p (x) - q (x) ∣ .

For unit rays we use

d_{ray} ([ψ], [ϕ]) = ∣ z ∣ = 1 min ∥ ψ - z ϕ ∥ .

Displayed formulas in this passage

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$H_{L} = q \in L ⨂ C^{2} .$
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$M^{S}_{κ} = ⟨ κ ∣_{S} \otimes I_{L ∖ S}, b^{S}_{ψ} (κ) = M^{S}_{κ} ψ^{2} .$
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$ψ^{S}_{L, κ} = \frac{M ^{S} _{κ} ψ}{b ^{S} _{ψ} ( κ )} .$
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$d_{TV} (p, q) = \frac{1}{2} x \sum ∣ p (x) - q (x) ∣ .$
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$d_{ray} ([ψ], [ϕ]) = ∣ z ∣ = 1 min ∥ ψ - z ϕ ∥ .$