Parameter estimation for mixed states from a single copy

2007/02/28 by Thomas Konrad, Otfried Gühne, Jürgen Audretsch +1
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum and electron transport phenomena #Spectroscopy and Quantum Chemical Studies #quant-ph

paper · pdf · doi:10.1103/physreva.75.062101

published as Phys. Rev. A 75, 062101 (2007) · 9 pages, 3 figures, v2: small changes, to appear in PRA

arxiv created 2007/05/08 · openalex publication_date 2007/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a single copy of a mixed state of the form \ensuremathρ=\ensuremathλ\ensuremathρ₁+(1\ensuremath-\ensuremathλ)\ensuremathρ₂, what is the optimal measurement to estimate the parameter \ensuremathλ if \ensuremathρ₁ and \ensuremathρ₂ are known? We present a general strategy to obtain the optimal measurements employing a Bayesian estimator. The measurements are chosen to minimize the deviation between the estimated value and the true value of \ensuremathλ. We explicitly determine the optimal measurements for a general two-dimensional system and for important higher dimensional cases.

Citations

• Universal Programmable Quantum State Discriminator that is Optimal for Unambiguously Distinguishing between Unknown States
• Classical randomness in quantum measurements
• Reduction theorems for optimal unambiguous state discrimination of density matrices
• Separability of mixed states: necessary and sufficient conditions