Physics – Quantum Physics
Scientific paper
2000-06-01
J. Phys. A. 34 (7 Sept 2001) 7029-7046
Physics
Quantum Physics
Sixteen pages, six postscript figures, we include an additional analysis (in sec. III D 3) for N = 2 copies of the 3-level qua
Scientific paper
10.1088/0305-4470/34/35/328
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.
Slater Paul B.
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