Okon, Sudarsky & Wiedemann argue the compensating-preparer mechanism only restores statistical, not individual-outcome, conservation

physicsquantum-mechanicsquantum-measurementconservation-lawsquant-phphysics.hist-ph

Okon, Sudarsky & Wiedemann (2026, arXiv:2610.29804) grant, for the sake of argument, the framework Collins & Popescu (Quantum 9, 1815, 2025) propose for restoring conservation outcome-by-outcome — a "preparer" system entangled with the measured one so that whatever the measured system gains, the preparer loses. They argue the mechanism does not deliver what it claims even on its own terms.

For the measured system's reduced state to approximate an ordinary pure superposition, the preparer's own initial state cannot be an eigenstate of the conserved quantity; it must itself be in a broad superposition. That superposition is not collapsed to a definite value by the measurement either — the preparer's post-measurement state is just a shifted version of the same kind of superposition. The preparer therefore never possesses a definite value of the conserved quantity, neither before nor after the measurement, so there is no definite amount that can be said to have been transferred between the two subsystems. What is shown to compensate is only the probability distributions over outcomes — the familiar statistical notion of conservation the proposal explicitly set out to go beyond.

This is the second of two independent grounds on which the paper rejects the mechanism, alongside the separate reference-frame regress argument (claim-okon-sudarsky-wiedemann-reference-frame-regress-undermines-preparer-requirement). A further, more specific failure of the same mechanism — that it cannot be extended to several noncommuting conserved quantities at once — is argued with a worked example in claim-okon-sudarsky-wiedemann-noncommuting-conserved-quantities-break-compensation-mechanism.