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We investigate the statistical arrow of time for a quantum system being monitored by a sequence of measurements. For a continuous qubit measurement example, we demonstrate that time-reversed evolution is always physically possible, provided that the measurement record is also negated. Despite this restoration of dynamical reversibility, a statistical arrow of time emerges, and may be quantified by the log-likelihood difference between forward and backward propagation hypotheses. We then show that such reversibility is a universal feature of nonprojective measurements, with forward or backward Janus measurement sequences that are time-reversed inverses of each other.


This article was originally published in Physical Review Letters, volume 119, in 2017. DOI:10.1103/PhysRevLett.119.220507

Peer Reviewed



American Physical Society



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