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)emb...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 R^((N^2)-1), and we find that an orthogonal measurement is an(N- 1)-dimensional projector operator on 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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11405136 and 11547311)the Fundamental Research Funds for the Central Universities of China(Grant No.2682014BR056)
文摘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 R^((N^2)-1), and we find that an orthogonal measurement is an(N- 1)-dimensional projector operator on 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.
