Positive reduction from spectra

Abstract

We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear inequalities, which the spectrum has to verify. Our conditions become explicit when one of the two subsystems is a qubit, as well as for further sets of states. Finally, we introduce a family of simple entanglement criteria for spectra, closely related to the reduction and positive partial transpose criteria, which also provide new insight into the set of spectra that guarantee separability or positivity of the partial transpose.

Linear Algebra and its Applications (2015)

References in corpus (13)

• Quantum entanglement
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Cited by in corpus (11)

• Maximal Coherence and the Resource Theory of Purity
• Random matrix techniques in quantum information theory
• Characterizing the boundary of the set of absolutely separable states and their generation via noisy environments
• Absolutely separating quantum maps and channels
• Efficient nonlinear witnessing of non-absolutely separable states with lossy detectors
• Thresholds for reduction-related entanglement criteria in quantum information theory
• Absolutely $k$-Incoherent Quantum States and Spectral Inequalities for Factor Width of a Matrix
• Convex set of quantum states with positive partial transpose analysed by hit and run algorithm
• Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses
• Is absolute separability determined by the partial transpose?
• On the extreme points of sets of absolulely separable and PPT states