Purity-bounded uncertainty relations in multidimensional space -- generalized purity

Details Purity-bounded uncertainty relations in multidimensional space -- generalized purity Purity-bounded uncertainty relations in multidimensional space -- generalized purity

2004-11-09

arxiv.org/abs/quant-ph/0411067v5

J. Phys. A: Math. Gen., vol. 38, pp. 6393-6403 (2005)

Physics

Quantum Physics

12 pages, 2 figures. draft version, to appear in J. Phys. A Partially based on a poster "Multidimensional uncertainty relation

Scientific paper

10.1088/0305-4470/38/28/012

Uncertainty relations for mixed quantum states (precisely, purity-bounded position-momentum relations, developed by Bastiaans and then by Man'ko and Dodonov) are studied in general multi-dimensional case. An expression for family of mixed states at the lower bound of uncertainty relation is obtained. It is shown, that in case of entropy-bounded uncertainty relations, lower-bound state is thermal, and a transition from one-dimensional problem to multi-dimensional one is trivial. Results of numerical calculation of the relation lower bound for different types of generalized purity are presented. Analytical expressions for general purity-bounded relations for highly mixed states are obtained.

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