Authors derive genuine multientropy for Lifshitz states as mutual information plus negativity, obtain its non-integer Rényi continuation, and prove dihedral invariants equal Rényi reflected entropies for general tripartite pure states.
A matrix realignment method for recognizing entanglement
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any separable state, the sum of the singular values of the matrix should be less than or equal to 1. This condition provides a very simple, computable necessary criterion for separability, and shows powerful ability to identify most bound entangled states discussed in the literature. As a byproduct of the criterion, we give an estimate for the degree of entanglement of the quantum state.
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Implements PnCP maps from non-SOS polynomials, proves they are indecomposable and boundary-localized, shows inequivalence to most known maps, and demonstrates detection of PPT entangled states missed by other criteria.
Derives necessary and sufficient criterion for entanglement detection via multiple product-state fidelities and characterizes the joint separable numerical range for pairs of such states.
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
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Genuine multientropy, dihedral invariants and Lifshitz theory
Authors derive genuine multientropy for Lifshitz states as mutual information plus negativity, obtain its non-integer Rényi continuation, and prove dihedral invariants equal Rényi reflected entropies for general tripartite pure states.