Conditional Action and Quantum Versions of Maxwell's Demon

Abstract

We propose a new way of looking at the quantum Maxwell's demon problem in terms of conditional action. A ``conditional action'' on a system is a unitary time evolution, selected according to the result of a previous measurement, which can reduce the entropy of the system. However, any conditional action can be realized by an (unconditional) unitary time evolution of a larger system and a subsequent Luders measurement, whereby the entropy of the entire system is either increased or remains constant. We give some examples that illustrate and confirm our proposal, including the erasure ofNqubits and the Szilard engine, thus relating the present approach to the Szilard principle and the Landauer principle that have been discussed as possible solutions of the Maxwell's demon problem.