Advances in Quantum Detection

Concha, J.I.; Poor, H. Vincent

doi:10.1007/978-1-4757-3789-9_7

Cited by 2 publications

(3 citation statements)

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“…Theorem 9 of section IV combines ideas of Holevo [37], Curlander [38], and Concha & Poor [39][40][41] to give mathematically concise upper and lower distinguishability bounds for arbitrary ensembles of mixed quantum states. Employing an approximate minimal principle, a suboptimal measurement is derived which has a failure rate within a factor of two of the optimal by construction.…”

Section: Ia Resultsmentioning

confidence: 99%

“…Remark: The approximate cost function (24) is a somewhat-disguised modification of the minimal principle of Concha and Poor [39][40][41], which was reverse-engineered to reproduce the ad-hoc mixed-state PGM. The measurement (25) is an example of a mixed-state Belavkin weighted measurement.…”

Section: By Bessel's Inequalitymentioning

confidence: 99%

“…5 The approximate cost function (24) for the quadratic measurement is within a factor of two of the function P fail (M k ). (The corresponding cost functions for the pure and mixed-states PGMs [39][40][41]45] admit no such comparison. )…”

Section: Reflections On the Quadratic Weightingmentioning

confidence: 99%

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Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo–Curlander bounds

Tyson

2009

Journal of Mathematical Physics

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We prove a concise factor-of-two estimate for the failure-rate of optimally distinguishing an arbitrary ensemble of mixed quantum states, generalizing work of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis, MIT, 1979]. A modification of the minimal principle of Concha and Poor [Proceedings of the 6th International Conference on Quantum Communication, Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive a sub-optimal measurement which has an error rate within a factor of two of the optimal by construction. This measurement is quadratically weighted, and has appeared as the first iterate of a sequence of measurements proposed by Ježek,Řeháček, and Fiurášek [Phys. Rev. A 65, 060301]. Unlike the so-called "pretty good" measurement, it coincides with Holevo's asymptotically-optimal measurement in the case of non-equiprobable pure states. A quadraticallyweighted version of the measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] is proven. Bounds on the distinguishability of syndromes in the sense of Schumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as a corollary. An appendix relates our bounds to the trace-Jensen inequality. * jonetyson@X.Y.Z, where X=post, Y=Harvard, Z=edu

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Section: Ia Resultsmentioning

confidence: 99%