Abstract
Monogamy and polygamy relations of quantum entanglement characterize the sharing and distribution of entanglement in a multipartite system. Multiqubit entanglement can be characterized entirely with bipartite combinations by saturating the monogamy and polygamy inequalities. In this paper, we tighten monogamy and polygamy constraints for the squared convex-roof extended negativity and its dual measure by employing a genetic algorithm. This evolutionary algorithm optimizes inequality residual functions to improve the monogamy and polygamy relations of these entanglement measures.
Highlights
One distinct property of entanglement is its limited shareability
Our main focus in this paper is to tighten the monogamy and polygamy inequalities based on the squared convex-roof extended negativity (SCREN) and the SCREN of assistance (SCRENoA)13 for multipartite qubit systems
Entanglement negativity, which is based on the positive partial transposition (PPT) criterion, holds the monogamy relation for some qudit systems as well13
Summary
One distinct property of entanglement is its limited shareability. This property is eloquently captured by the monogamy relation of entanglement. This statement can be further generalized to a multipartite scenario and similar restrictions on the amount of individual correlations can be imposed10–13 These monogamy relations provide a way to characterize different types of entanglement sharing. Survivals demonstrating higher fitness for the objective function are passed on to the generation (either directly, or after crossover and mutation with other individuals), whereas the weaker individuals are removed. Our main focus in this paper is to tighten the monogamy and polygamy inequalities based on the squared convex-roof extended negativity (SCREN) and the SCREN of assistance (SCRENoA) for multipartite qubit systems. We optimize key parameters of the residual expression to tighten the inequality using the GA This framework provides monogamy and polygamy inequalities that are significantly tighter than the other known bounds
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