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Physical Review Letters

Reversibility in quantum measurement processes

Masahito Ueda, Masahiro Kitagawa

Published Jun 8, 1992• 89 citations
Publisher

Abstract

A measurement process is logically reversible if the premeasurement density operator of the measured system can be calculated from the postmeasurement density operator and the readout of the measuring apparatus. We show that the continuous-measurement version of a quantum counter, unlike the conventional photon counter, performs a logically reversible measurement. The physical origin for such a distinction is found to be sensitivity to vacuum field fluctuations.

DOI
10.1103/physrevlett.68.3424

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A measurement process is logically reversible if the premeasurement density operator of the measured system can be calculated from the postmeasurement density operator and the readout of the measuring apparatus. We show that the continuous-measurement version of a quantum counter, unlike the conventional photon counter, performs a logically reversible measurement. The physical origin for such a distinction is found to be sensitivity to vacuum field fluctuations.
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A quantum measurement is logically reversible if the premeasurement density operator of the measured system can be calculated from the postmeasurement density operator and from the outcome of the measurement. This paper analyzes why many quantum measurements are logically irreversible, shows how to make them logically reversible, and discusses reversing measurement that returns the postmeasurement state to the premeasurement state by another measurement (physical reversibility). Reversing measurement and unitarily reversible quantum operation are compared from the viewpoint of error correction in quantum computation. 1.
A measurement process is logically reversible if the premeasurement density operator of the measured system is uniquely determined from the postmeasurement density operator and the outcome of the measurement. This paper analyzes the necessary and sufficient condition for a measurement process to be logically reversible and discusses specific examples on quantum-nondemolition measurements, quantum counting, and measurement of spin systems. It is shown that for any sharp measurement we can construct a logically reversible measurement that continuously approaches the sharp measurement with a decrease in the measurement error. A general condition for a measurement process to be reversed by another with a nonzero probability of success is given, and the implications of such physical reversibility are discussed. \textcopyright{} 1996 The American Physical Society.
Four types of photon counters are discussed in terms of information, fidelity, and physical reversibility: conventional photon counter, quantum counter, and their quantum nondemolition (QND) versions. It is shown that when a photon field to be measured is in an arbitrary superposition of vacuum and one-photon states, the quantum counter is the most reversible, the QND version of conventional photon counter provides the most information, and the QND version of the quantum counter causes the smallest state change. Our results suggest that the physical reversibility of a counter tends to decrease the amount of information obtained by the counter.