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

**Quantum lost property : a possible operational meaning for the Hilbert-Schmidt product.** / Pusey, Matthew F.; Rudolph, Terry.

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

Pusey, MF & Rudolph, T 2012, 'Quantum lost property: a possible operational meaning for the Hilbert-Schmidt product', *Physical Review A*, vol. 86, 044301. https://doi.org/10.1103/PhysRevA.86.044301

Pusey, M. F., & Rudolph, T. (2012). Quantum lost property: a possible operational meaning for the Hilbert-Schmidt product. *Physical Review A*, *86*, [044301]. https://doi.org/10.1103/PhysRevA.86.044301

Pusey MF, Rudolph T. Quantum lost property: a possible operational meaning for the Hilbert-Schmidt product. Physical Review A. 2012 Oct 18;86. 044301. https://doi.org/10.1103/PhysRevA.86.044301

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title = "Quantum lost property: a possible operational meaning for the Hilbert-Schmidt product",

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.",

author = "Pusey, {Matthew F.} and Terry Rudolph",

note = "{\textcopyright} 2012 American Physical Society",

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AU - Rudolph, Terry

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N2 - 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.

AB - 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.

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