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Bures Metrics for Certain HighDimensional Quantum Systems  Paul B. Slater
;  Date: 
23 Oct 1997  Journal:  Phys.Lett. A244 (1998) 3542  Subject:  quantph  Affiliation:  University of California, Santa Barbara  Abstract:  Hubner’s formula for the Bures (statistical distance) metric is applied to both a oneparameter and a twoparameter series (n=2,...,7) of sets of 2^n x 2^n density matrices. In the doublyparameterized series, the sets are comprised of the nfold tensor products  corresponding to n independent, identical quantum systems  of the 2 x 2 density matrices with real entries. The Gaussian curvatures of the corresponding Bures metrics are found to be constants (4/n). In the second series of 2^n x 2^n density matrices studied, the singlyparameterized sets are formed  following a study of Krattenthaler and Slater  by averaging with respect to a certain Gibbs distribution, the nfold tensor products of the 2 x 2 density matrices with complex entries. For n = 100, we are also able to compute the Bures distance between two arbitrary (not necessarily neighboring) density matrices in this particular series, making use of the eigenvalue formulas of Krattenthaler and Slater, together with the knowledge that the 2^n x 2^n density matrices in this series commute.  Source:  arXiv, quantph/9710055  Services:  Forum  Review  PDF  Favorites 


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