Bipartite quantum systems: on the realignment criterion and beyond

Abstract

Inspired by the `computable cross norm' or `realignment' criterion, we propose a new point of view about the characterization of the states of bipartite quantum systems. We consider a Schmidt decomposition of a bipartite density operator. The corresponding Schmidt coefficients, or the associated symmetric polynomials, are regarded as quantities that can be used to characterize bipartite quantum states. In particular, starting from the realignment criterion, a family of necessary conditions for the separability of bipartite quantum states is derived. We conjecture that these conditions, which are weaker than the parent criterion, can be strengthened in such a way to obtain a new family of criteria that are independent of the original one. This conjecture is supported by numerical examples for the low dimensional cases. These ideas can be applied to the study of quantum channels, leading to a relation between the rate of contraction of a map and its ability to preserve entanglement.

19 pages, 4 figures, improved version

References in corpus (17)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Separability criterion and inseparable mixed states with positive partial transposition
• General Entanglement Breaking Channels
• Further results on the cross norm criterion for separability
• Separable states are more disordered globally than locally
• Dividing Quantum Channels
• Some Properties of the Computable Cross Norm Criterion for Separability
• Qubit Entanglement Breaking Channels
• Nonlinear entanglement witnesses
• Optimal entanglement witnesses based on local orthogonal observables
• Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion
• Entanglement Detection by Local Orthogonal Observables
• Entanglement detection beyond the cross-norm or realignment criterion
• A class of inequalities inducing new separability criteria for bipartite quantum systems
• On approximation of quantum channels
• Remarks on the Cross Norm Criterion for Separability

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• Unitary quantum gates, perfect entanglers and unistochastic maps
• Entanglement detection via tighter local uncertainty relations
• On the classical capacity of quantum Gaussian channels
• BROTOCs and Quantum Information Scrambling at Finite Temperature
• On the relation between Schmidt coefficients and entanglement
• Scrambling and operator entanglement in local non-Hermitian quantum systems
• A note on the realignment criterion
• Enhanced realignment criterion vs. linear entanglement witnesses
• Detection of bound entanglement in continuous variable systems
• Realignment Entanglement Criterion for Continuous Bipartite Symmetric Quantum States
• Channel discrimination power of bipartite quantum states
• Locality, Correlations, Information, and non-Hermitian Quantum Systems
• Correlation Minor Norms, Entanglement Detection and Discord
• Physical realization of realignment criteria using structural physical approximation
• Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps