Quantum measurement in coherence-vector representation

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 (N2 − 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.