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Increased Efficiency of Quantum State Estimation Using Non-Separable Measurements | Paul B. Slater
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1 Jun 2000 | Journal: | J. Phys. A. 34 (7 Sept 2001) 7029-7046 | Subject: | Quantum Physics; Data Analysis, Statistics and Probability | quant-ph physics.data-an | Affiliation: | University of California | Abstract: | We address the "major open problem" of evaluating how much increased efficiency in estimation is possible using non-separable, as opposed to separable, measurements of N copies of m-level quantum systems. First, we study the six cases m = 2, N = 2,...,7 by computing the the 3 x 3 Fisher information matrices for the corresponding optimal measurements recently devised by Vidal et al (quant-ph/9812068) for N = 2,...,7. We obtain simple polynomial expressions for the ("Gill-Massar") traces of the products of the inverse of the quantum Helstrom information matrix and these Fisher information matrices. The six traces all have minima of 2 N -1 in the pure state limit, while for separable measurements (quant-ph/9902063), the traces can equal N, but not exceed it. Then, the result of an analysis for m = 3, N = 2 leads us to conjecture that for optimal measurements for all m and N, the "Gill-Massar trace" achieves a minimum of (2N-1)(m-1) in the pure state limit. | Source: | arXiv, quant-ph/0006009 | Other source: | [GID 853224] quant-ph/0006009 | Services: | Forum | Review | PDF | Favorites |
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