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

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

In: Physical Review A, Vol. 86, 044301, 18.10.2012.

Research output: Contribution to journalArticlepeer-review

Harvard

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

APA

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

Vancouver

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

Author

Pusey, Matthew F. ; Rudolph, Terry. / Quantum lost property : a possible operational meaning for the Hilbert-Schmidt product. In: Physical Review A. 2012 ; Vol. 86.

Bibtex - Download

@article{6c8631f53e354cfeb345411718b20da0,
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",
year = "2012",
month = oct,
day = "18",
doi = "10.1103/PhysRevA.86.044301",
language = "English",
volume = "86",
journal = "Physical Review A",
issn = "1050-2947",
publisher = "American Physical Society",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Quantum lost property

T2 - a possible operational meaning for the Hilbert-Schmidt product

AU - Pusey, Matthew F.

AU - Rudolph, Terry

N1 - © 2012 American Physical Society

PY - 2012/10/18

Y1 - 2012/10/18

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.

U2 - 10.1103/PhysRevA.86.044301

DO - 10.1103/PhysRevA.86.044301

M3 - Article

VL - 86

JO - Physical Review A

JF - Physical Review A

SN - 1050-2947

M1 - 044301

ER -