Bipartite quantum measurements with optimal single-sided distinguishability

• URL: http://arxiv.org/abs/2010.14868v3
• Date: Fri, 23 Apr 2021 15:53:58 GMT
• Title: Bipartite quantum measurements with optimal single-sided distinguishability
• Authors: Jakub Czartowski, Karol \.Zyczkowski
• Abstract summary: We look for a basis with optimal single-sided mutual state distinguishability in $Ntimes N$ Hilbert space. In the case $N=2$ of a two-qubit system our solution coincides with the elegant joint measurement introduced by Gisin. We show that the one-party measurement that distinguishes the states of an optimal basis of the composite system leads to a local quantum state tomography.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We analyse orthogonal bases in a composite $N\times N$ Hilbert space describing a bipartite quantum system and look for a basis with optimal single-sided mutual state distinguishability. This condition implies that in each subsystem the $N^2$ reduced states form a regular simplex of a maximal edge length, defined with respect to the trace distance. In the case $N=2$ of a two-qubit system our solution coincides with the elegant joint measurement introduced by Gisin. We derive explicit expressions of an analogous constellation for $N=3$ and provide a general construction of $N^2$ states forming such an optimal basis in ${\cal H}_N \otimes {\cal H}_N$. Our construction is valid for all dimensions for which a symmetric informationally complete (SIC) generalized measurement is known. Furthermore, we show that the one-party measurement that distinguishes the states of an optimal basis of the composite system leads to a local quantum state tomography with a linear reconstruction formula. Finally, we test the introduced tomographical scheme on a complete set of three mutually unbiased bases for a single qubit using two different IBM machines.

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