bibkey: codex2026correlationtax
authors: Codex implementation worker
year: 2026
title: Coherent premeasurement and the correlation-tax identity
doi: null
url: https://github.com/the-omega-institute/trureturing
claim: A repository derivation of coherent-copy marginals, entropy preservation, and the correlation-tax identity.
strata_touched:
  - D5/S3/Quantum/Information/CoherentCopyCorrelationTax
license: citation-only
triage: anchor

Coherent premeasurement

Verified locator

This entry records the repository derivation at the canonical repository locator: https://github.com/the-omega-institute/trureturing The formal source is D5/S3/Quantum/Information/CoherentCopyCorrelationTax.lean. It treats the coherent matrix V rho V*, where V sends each basis vector i to (i,i). The formal derivation uses the repository’s density states, partial traces, entropy, and relative entropy. The mathematical identity is not claimed to be novel.

The derivation retains all off-diagonal entries on the correlated subspace. Tracing out either tensor factor removes those coherences, while the entropy of the joint state equals the input entropy. The construction is distinct from the classical mixture of records, whose joint entropy already equals the diagonal entropy.