Quantum Reversibility Is Relative, Or Do Quantum Measurements Reset Initial Conditions?

TL;DR

This paper explores how quantum measurements influence the reversibility of quantum evolution, showing that information gain can cause irreversibility even in unitary dynamics, unlike classical systems.

Contribution

It demonstrates that quantum irreversibility depends on information retention, contrasting classical and quantum dynamics, and introduces quantum discord as a measure of information's impact on reversibility.

Findings

Quantum reversibility is relative and depends on information retention.

Recording measurement outcomes resets initial conditions, affecting reversibility.

Quantum discord quantifies the influence of information dissemination on reversibility.

Abstract

I compare the role of the information in the classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics reversibility is unaffected by the observer's retention of the information about the measurement outcome. By contrast -- even though quantum dynamics is unitary, hence, reversible -- reversing quantum evolution that led to a measurement becomes in principle impossible for an observer who keeps the record of its outcome. Thus, quantum irreversibility can result from the information gain rather than just its loss -- rather than just an increase of the (von Neumann) entropy. Recording of the outcome of the measurement resets, in effect, initial conditions within the observer's (branch of) the Universe. Nevertheless, I also show that observer's friend -- an agent who knows what measurement was successfully carried out and can confirm that the observer knows the outcome but resists his curiosity and does not find out the result -- can, in principle, undo the measurement. This relativity of quantum reversibility sheds new light on the origin of the arrow of time and elucidates the role of information in classical and quantum physics. Quantum discord appears as a natural measure of the extent to which dissemination of information about the outcome affects the ability to reverse the measurement.