Manuscript Em03-C@1 · Em03-C-v1.tex · example · 47dd71ec

Example: Same number law, different coherences

Joint count certificates and bounded diagnostics › Information that number records miss · lines 2059–2074

The states

∣ ψ_{\pm} ⟩ = \frac{∣ 1 , 0 ⟩ \pm ∣ 0 , 1 ⟩}{2}

have identical joint number laws. They are orthogonal. For cutoffs $a_{i} \geq 1$ , their exact finite encodings have a two-qubit $X \otimes X$ expectation of $+ 1$ and $- 1$ , respectively, on the two active qubits; unused qubits are zero. A Pauli setting distinguishes them, whereas any number-diagonal record does not.

These are synthetic controls, not states claimed to be produced by the inherited Hawking model.

Displayed formulas in this passage

unlabeled · line 2061
$∣ ψ_{\pm} ⟩ = \frac{∣ 1 , 0 ⟩ \pm ∣ 0 , 1 ⟩}{2}$

Nearby in this section

section: Information that number records miss
figure: Phase missed by number records