Separability, entanglement and full families of commuting normal matrices

Abstract

We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure states constituting a decomposition of the considered mixture. The method reproduces many known entanglement and/or separability criteria, and provides yet another geometrical characterization of mixed separable states.

arXiv comment14 pages, some typos corrected, a reference added, in print in Phys. Rev. A

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Cited by in corpus (13)

• Quantum entanglement
• Structural approximations to positive maps and entanglement breaking channels
• Four-qubit entangled symmetric states with positive partial transpositions
• Entangled symmetric states of N qubits with all positive partial transpositions
• Facial structures for various notions of positivity and applications to the theory of entanglement
• Quantum states with strong positive partial transpose
• Searching for extremal PPT entangled states
• Reduced and projected two-particle entanglement at finite temperatures
• Iterations of nonlinear entanglement witnesses
• Existence of product vectors and their partial conjugates in a pair of spaces
• Many body physics from a quantum information perspective
• Entanglement at finite temperatures in the electronic two-particle interferometer
• Separability in terms of a single entanglement witness