Complementarity in generic open quantum systems

Abstract

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian observable and phase as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as a lower bound on {\it entropy excess}, $X$, the difference between the entropy of one variable, typically the number, and the knowledge of its complementary variable, typically the phase, where knowledge of a variable is defined as its relative entropy with respect to the uniform distribution. In the case of finite dimensional systems, a weighting of phase knowledge by a factor $\mu$ ($>1$) is necessary in order to make the bound tight, essentially on account of the POVM nature of phase as defined here. Numerical and analytical evidence suggests that $\mu$ tends to 1 as system dimension becomes infinite. We study the effect of non-dissipative and dissipative noise on these complementary variables for oscillator as well as atomic systems.

18 pages, 15 figures; accepted for publication in Modern Physics Letters A

References in corpus (6)

• The squeezed generalized amplitude damping channel
• Geometric Phase of a qubit interacting with a squeezed-thermal bath
• Complementarity in quantum systems
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• Phase diffusion pattern in quantum nondemolition systems
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Cited by in corpus (7)

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• Quantum entropy of systems described by non-Hermitian Hamiltonians
• Quasiprobability distributions in open quantum systems: spin-qubit systems
• Quantum phase properties of photon added and subtracted displaced Fock states
• Embedding quantum systems with a non-conserved probability in classical environments
• An investigation on the nonclassical and quantum phase properties of a family of engineered quantum states