Compatibility Relations between the Reduced and Global Density Matrixes

Details Compatibility Relations between the Reduced and Global Density Matrixes Compatibility Relations between the Reduced and Global Density Matrixes

2004-03-22

arxiv.org/abs/quant-ph/0403151v1

Physics

Quantum Physics

14 pages

Scientific paper

10.1103/PhysRevA.72.054302

It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body quantum entanglement which is one of the focuses of current quantum information theory. We give several results on the necessary compatibility relations between a set of reduced density matrixes, including: (i) compatibility conditions for the one-party reduced density matrixes of any $N_A\times N_B$ dimensional bi-partite mixed quantum state, (ii) compatibility conditions for the one-party and two-party reduced density matrixes of any $N_A\times N_B\times N_C$ dimensional tri-partite mixed quantum state, and (iii) compatibility conditions for the one-party reduced matrixes of any $M$-partite pure quantum state with the dimension $N^{\otimes M}$.

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