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Quantum measurement in coherence-vector representation

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Abstract

We consider the quantum measurements on a finite quantum system in coherence-vector representation. In this representation, all the density operators of an N-level (N ⩾ 2) quantum system constitute a convex set M (N) embedded in an (N 2 − 1)-dimensional Euclidean space \(\mathbb{R}^{N^2 - 1}\), and we find that an orthogonal measurement is an (N − 1)-dimensional projector operator on \(\mathbb{R}^{N^2 - 1}\). The states unchanged by an orthogonal measurement form an (N − 1)-dimensional simplex, and in the case when N is prime or power of prime, the space of the density operator is a direct sum of (N + 1) such simplices. The mathematical description of quantum measurement is plain in this representation, and this may have further applications in quantum information processing.

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  1. School of Physical Science and Technology, Southwest Jiaotong University, Chengdu, 610031, China

    Tao Zhou

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Correspondence to Tao Zhou.

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Zhou, T. Quantum measurement in coherence-vector representation. Sci. China Phys. Mech. Astron. 59, 640301 (2016). https://doi.org/10.1007/s11433-016-5789-5

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