Towards variance-matrix characterization of complementarity relations in a continuous variable system

Abstract

We discuss complementarity relations in a bipartite continuous variable system. Building up from the work done on discrete d-dimensional systems, we prove that for symmetric two-mode states, quantum complementarity relations can be put in a simple relation with the elements of the variance matrix. When this condition is not satisfied, such a connection becomes non-trivial. Our investigation is the first step towards an operative characterization of the complementarity in a scenario that has not been investigated so far.

Keywords:

• complementarity relations
• entanglement
• single-body properties
• continuous variable systems
• quantum optics

Acknowledgements

We thank M.S. Kim for helpful discussions and encouragement regarding this work. SS thanks J. Bergou for having kindly sent him a preprint of 8. MP thanks EPSRC for financial support (EP/G004579/1). SS is supported by DEL.