https://doi.org/10.1140/epjd/e2009-00049-1
Complementarity in atomic (finite-level quantum) systems: an information-theoretic approach
1
Poornaprajna Institute of Scientific Research, Sadashiva
Nagar, 560080 Bangalore, India
2
Raman Research Institute, Sadashiva Nagar, 560080 Bangalore, India
Corresponding author: a srik@rri.res.in
Received:
31
May
2008
Revised:
24
November
2008
Published online:
13
February
2009
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 significant 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.
PACS: 03.67.-a – Quantum information / 03.65.Ta – Foundations of quantum mechanics; measurement theory / 03.65.Yz – Decoherence; open systems; quantum statistical methods
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009