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arXiv:1903.11355 · Physical Review A

Superactivation of monogamy relations for nonadditive quantum correlation measures

Zhi‐Xiang Jin, Shao-Ming Fei

Published Mar 26, 2019• 30 citations
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Abstract

We investigate the general monogamy and polygamy relations satisfied by quantum correlation measures. We show that there exist two real numbers $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ such that for any quantum correlation measure $Q,{Q}^{x}$ is monogamous if $x\ensuremath{\ge}\ensuremath{\alpha}$ and polygamous if $0\ensuremath{\le}x\ensuremath{\le}\ensuremath{\beta}$ for a given multipartite state $\ensuremath{\rho}$. For $\ensuremath{\beta}<x<\ensuremath{\alpha}$, we show that the monogamy relation can be superactivated by finite $m$ copies ${\ensuremath{\rho}}^{\ensuremath{\bigotimes}m}$ of $\ensuremath{\rho}$ for nonadditive correlation measures. As a detailed example, we use the negativity as the quantum correlation measure to illustrate such superactivation of monogamy properties. A tighter monogamy relation is presented at last.

DOI
10.1103/physreva.99.032343

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The monogamy relation for quantum correlations is not satisfied by all measures for all multiparty quantum states. We prove that an arbitrary quantum state which is nonmonogamous for negativity will become monogamous if a finite number of copies of the same state is provided. We refer to this as activation of nonmonogamous states. We also show that multiple copies of a state satisfy monogamy for negativity if it does so for a single copy. The results are true for all quantum states of an arbitrary number of parties. Moreover, we find that for a three-qubit pure state, we can find another state such that they individually violate the monogamy relation for negativity and when taken together they can satisfy the three-party monogamy relation. This holds for all three-qubit pure states except 11%1 states from the W class, while it is true for all three-qubit pure states when a four-party monogamy relation is used to check for their activation. We connect monogamy of negativity with genuine multipartite entanglement.
Abstract We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy relations for the r-power of the measure. We show in a uniformed manner that the generalized monogamy and polygamy relations are transitive to other powers of the measure in weighted forms We demonstrate that our weighted monogamy and polygamy relations are stronger than recently available relations. Comparisons are given in detailed examples which show that our results are stronger in both situations.
Abstract This research offers a comprehensive approach to strengthening both monogamous and polygamous relationships within the context of quantum correlations in multipartite quantum systems. We present the most stringent bounds for both monogamy and polygamy in multipartite systems compared to recently established relations. We show that whenever a bound is given (named it monogamy or polygamy), our bound indexed by some parameter s will always be stronger than the given bound. The study includes detailed examples, highlighting that our findings exhibit greater strength across all existing cases in comparison.
We study the distribution of quantum correlations characterized by monogamy relations in multipartite systems. By using the Hamming weight of the binary vectors associated with the subsystems, we establish a class of monogamy inequalities for multiqubit entanglement based on the α\alphaαth (α≥2\alpha\geq 2α≥2) power of concurrence, and a class of polygamy inequalities for multiqubit entanglement in terms of the β\betaβth (0≤β≤20\leq \beta\leq20≤β≤2) power of concurrence and concurrence of assistance. Moveover, we give the monogamy and polygamy inequalities for general quantum correlations. Application of these results to quantum correlations like squared convex-roof extended negativity (SCREN), entanglement of formation and Tsallis-qqq entanglement gives rise to either tighter inequalities than the existing ones for some classes of quantum states or less restrictions on the quantum states. Detailed examples are presented.
The monogamy and polygamy properties of quantum entanglement characterize fundamental constraints on the distribution of entanglement in multipartite quantum systems. In this paper, we investigate tighter monogamy and polygamy relations for multipartite entanglement. By establishing a new mathematical inequality, we derive a family of improved monogamy and polygamy inequalities for tripartite quantum systems and further extend these results to general multipartite systems. Comparisons with existing results show that the obtained bounds are tighter. Illustrative examples are provided to demonstrate the effectiveness of the proposed relations.
Monogamy relation is one of the essential properties of quantum entanglement, which characterizes the distribution of entanglement in a multipartite system. By virtual of the unified-(q,s) entropy, we obtain some novel monogamy and polygamy inequalities in general class of entanglement measures. For the multiqubit system, a class of tighter monogamy relations are established in term of the α-th power of unified-(q,s) entanglement for α ≥ 1. We also obtain a class of tighter polygamy relations in the β-th (0 ≤ β ≤ 1) power of unified-(q,s) entanglement of assistance. Applying these results to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance, and Tsallis-q entanglement of assistance, we obtain the corresponding monogamy and polygamy relations. Typical examples are presented for illustration. Furthermore, the complementary monogamy and polygamy relations are investigated for the α-th (0 ≤ α ≤ 1) and β-th (β ≥ 1) powers of unified entropy, respectively, and the corresponding monogamy and polygamy inequalities are obtained.