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Physical Review A

Logical reversibility in quantum-nondemolition measurements

Ataç İmamoğlu

Published Jun 1, 1993• 40 citations
Publisher

Abstract

We show that it is possible to make a logically reversible quantum-nondemolition measurement of an optical-field photon number, where the measurement preserves all the information contained in the premeasurement wave function. The nonunitary dynamics of the proposed scheme is analyzed using a Monte Carlo wave-function approach.
DOI
10.1103/physreva.47.r4577

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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.
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.
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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.
This paper intends to clarify some issues in the theory of quantum measurement by taking advantage of the self-consistent quantum formulation of nonlinear optics. A quantum-nondemolition measurement of the photon number of an optical pulse can be performed with a nonlinear Mach-Zehnder interferometer followed by a balanced detector. The full quantum-mechanical treatment shows that the shortcut in the description of the quantum-mechanical measurement, the so-called ``collapse of the wave function,'' is not needed for a self-consistent interpretation of the measurement process. Coherence in the density matrix of the signal to be measured is progressively reduced with increasing accuracy of the photon-number determination. The quantum-nondemolition measurement is incorporated in the double-slit experiment and the contrast ratio of the fringes is found to decrease systematically with increasing information on the photon number in one of the two paths. The ``gain'' in the measurement can be made arbitrarily large so that postprocessing of the information can proceed classically.
Many so called paradoxes of quantum mechanics are clarified when the measurement equipment is treated as a quantized system. Every measurement involves nonlinear processes. Self consistent formulations of nonlinear quantum optics are relatively simple. Hence optical measurements, such as the quantum nondemolition (QND) measurement of photon number, are particularly well suited for such a treatment. It shows that the so called 'collapse of the wave function' is not needed for the interpretation of the measurement process. Coherence of the density matrix of the signal is progressively reduced with increasing accuracy of the photon number determination. If the QND measurement is incorporated into the double slit experiment, the contrast ratio of the fringes is found to decrease with increasing information on the photon number in one of the two paths.