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Logical Reversibility and Physical Reversibility in Quantum Measurement

M. Ueda

Published Jan 1, 1998• 3 citations
OpenAlex

Abstract

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.

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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 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.
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.
Quantum operations provide a general description of the state changes allowed by quantum mechanics. The reversal of quantum operations is important for quantum error–correcting codes, teleportation and reversing quantum measurements. We derive information–theoretic conditions and equivalent algebraic conditions that are necessary and sufficient for a general quantum operation to be reversible. We analyse the thermodynamic cost of error correction and show that error correction can be regarded as a kind of `Maxwell demon', for which there is an entropy cost associated with information obtained from measurements performed during error correction. A prescription for thermodynamically efficient error correction is given.