Quantum lost property: a possible operational meaning for the Hilbert-Schmidt product

Matthew F. Pusey; Terry Rudolph

doi:10.1103/PhysRevA.86.044301

Quantum lost property: a possible operational meaning for the Hilbert-Schmidt product

Matthew F. Pusey, Terry Rudolph

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Minimum-error state discrimination between two mixed states ρ and σ can be aided by the receipt of “classical side information” specifying which states from some convex decompositions of ρ and σ apply in each run. We quantify this phenomena by the average trace distance and give lower and upper bounds on this quantity as functions of ρ and σ. The lower bound is simply the trace distance between ρ and σ, trivially seen to be tight. The upper bound is √(1−tr(ρσ)), and we conjecture that this is also tight. We reformulate this conjecture in terms of the existence of a pair of “unbiased decompositions,” which may be of independent interest, and prove it for a few special cases. Finally, we point towards a link with a notion of nonclassicality known as preparation contextuality.

Original language	English
Article number	044301
Journal	Physical Review A
Volume	86
DOIs	https://doi.org/10.1103/PhysRevA.86.044301
Publication status	Published - 18 Oct 2012

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10.1103/PhysRevA.86.044301

PhysRevA.86.044301
© 2012 American Physical Society
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