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

摘要

We prove a concise factor-of-2 estimate for the failure rate of optimallydistinguishing an arbitrary ensemble of mixed quantum states, generalizing workof Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis,MIT, 1979]. A modification to the minimal principle of Cocha and Poor[Proceedings of the 6th International Conference on Quantum Communication,Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive asuboptimal measurement which has an error rate within a factor of 2 of theoptimal by construction. This measurement is quadratically weighted and hasappeared as the first iterate of a sequence of measurements proposed by Jezeket al. [Phys. Rev. A 65, 060301 (2002)]. Unlike the so-called pretty goodmeasurement, it coincides with Holevo's asymptotically optimal measurement inthe case of nonequiprobable pure states. A quadratically weighted version ofthe measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] isproven. Bounds on the distinguishability of syndromes in the sense ofSchumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as acorollary. An appendix relates our bounds to the trace-Jensen inequality.