Compatibility Relations between the Reduced and Global Density Matrixes

Abstract

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 $N^{\otimes M}$.

14 pages

References in corpus (6)

• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• Quantum dynamics as a physical resource
• One-qubit reduced states of a pure many-qubit state: polygon inequalities
• Quantum state transformations and the Schubert calculus
• Universal Measure of Entanglement

Cited by in corpus (5)

• Compatibility of subsystem states and convex geometry
• Spectrum conditions for symmetric extendible states
• Compatibility conditions from multipartite entanglement measures
• Entanglement transitivity problems
• Reducible Correlations in Dicke States