Logical reversibility in quantum measurement: General theory and specific examples

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. © 1996 The American Physical Society.