Abstract
We establish a characterization of multi-qubit entanglement constraints in terms of non-negative power of entanglement measures based on unified-(q, s) entropy. Using the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of tight monogamy inequalities of multi-qubit entanglement based on the αth-power of unified-(q, s) entanglement for α ≥ 1. For 0 ≤ β ≤ 1, we establish a class of tight polygamy inequalities of multi-qubit entanglement in terms of the βth-power of unified-(q, s) entanglement of assistance. Thus our results characterize the monogamy and polygamy of multi-qubit entanglement for the full range of non-negative power of unified entanglement.
Highlights
Quantum entanglement is a quintessential feature of quantum mechanics revealing the fundamental insights into the nature of quantum correlations
Since its inception, understanding the nature of quantum entanglement is at the heart of quantum information theory
Entanglement in bipartite quantum systems has been well studied with rich understanding, the situation becomes far more difficult for the case of multi-partite quantum entanglement, and only few are known for its characterization as well as its quantification
Summary
We establish a characterization of multi-qubit entanglement constraints in terms of non-negative power of entanglement measures based on unified-(q, s) entropy. It is an important task to have proper bipartite entanglement quantifications, besides tangle, showing tight monogamy and polygamy inequalities for efficient characterization of multi-party entanglements from different classes in multi-party and even in high-dimensional quantum systems. We provide a full characterization of multi-qubit entanglement monogamy and polygamy constraints in terms of non-negative power of entanglement measures based on unified entropy[24,25]. After providing notations and definitions about binary vectors and Hamming weight, we establish a class of tight monogamy inequalities in multi-qubit system based on the αth-power of unified-(q, s) entanglement for α ≥ 1.
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