Complementarity in atomic (finite-level quantum) systems: an information-theoretic approach

Abstract

We develop an information theoretic interpretation of the number-phase complementarity in atomic systems, where phase is treated as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as an upper bound on a sum of knowledge of these two observables for the case of two-level systems. A tighter bound characterizing the uncertainty relation is obtained numerically in terms of a weighted knowledge sum involving these variables. We point out that complementarity in these systems departs from mutual unbiasededness in two signalificant ways: first, the maximum knowledge of a POVM variable is less than log(dimension) bits; second, surprisingly, for higher dimensional systems, the unbiasedness may not be mutual but unidirectional in that phase remains unbiased with respect to number states, but not vice versa. Finally, we study the effect of non-dissipative and dissipative noise on these complementary variables for a single-qubit system.

16 pages

References in corpus (7)

• Concepts and methods in the theory of open quantum systems
• The squeezed generalized amplitude damping channel
• Geometric Phase of a qubit interacting with a squeezed-thermal bath
• Higher entropic uncertainty relations for anti-commuting observables
• Phase Diffusion in Quantum Dissipative Systems
• Phase diffusion pattern in quantum nondemolition systems
• An environment-mediated quantum deleter

Cited by in corpus (6)

• Entropic uncertainty relations - A survey
• Quasiprobability distributions in open quantum systems: spin-qubit systems
• Quantum phase properties of photon added and subtracted displaced Fock states
• Maximally informative ensembles for SIC-POVMs in dimension 3
• Complementarity in generic open quantum systems
• Complementarity in atomic and oscillator systems