Manuscript I-B@1 · I-B-v1.tex · section · 5357688f

A nontrivial finite history readout

What destructive clock reading does and does not do › A nontrivial finite history readout · lines 936–958

I-B@1#eq:history-isometry

The Page–Wootters literature motivates distinguishing extraction of conditional blocks from additional dynamical hypotheses PageWootters,CheungEn09. The following finite example proves exact conditioning without claiming a stationary-universe construction.

Choose any finite-dimensional $H_{X}$ , a self-adjoint $H_{X}^{gen}$ , and

U_{k} = exp (- i t_{k} H_{X}^{gen} /ℏ) .

Define the isometry

J : H_{X} ⟶ H_{C} \otimes H_{X}, J ∣ ψ ⟩ = \frac{1}{D} k = 0 \sum^{D - 1} ∣ τ_{k} ⟩ \otimes U_{k} ∣ ψ ⟩ .

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I-B@1#eq:history-isometry · line 950
$J : H_{X} ⟶ H_{C} \otimes H_{X}, J ∣ ψ ⟩ = \frac{1}{D} k = 0 \sum^{D - 1} ∣ τ_{k} ⟩ \otimes U_{k} ∣ ψ ⟩ .$
unlabeled · line 946
$U_{k} = exp (- i t_{k} H_{X}^{gen} /ℏ) .$

A nontrivial finite history readout

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