Tighter Constraints of Quantum Correlations Among Multipartite Systems

Jin-Hong Hao, Ya-Ya Ren, Qiao-Qiao Lv +2 more

Thiago Rodrigues de Oliveira

Chenxiao Wang, Limin Gao

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.

Rain Lenny, Dana Ben Porath, Eliahu Cohen

Despite their importance, there is an ongoing challenge characterizing multipartite quantum correlations. The Seevinck-Svetlichny (SS) and Mermin-Klyshko (MK) inequalities present constraints on correlations in multipartite systems, a violation of which allows to classify the correlations by using the nonseparability property. In this work we present refined Tsirelson (quantum) bounds on these inequalities, derived from inequalities stemming from a fundamental constraint, tightly akin to quantum uncertainty. Unlike the original, known inequalities, our bounds do not consist of a single constant point but rather depend on correlations in specific subsystems (being local correlations for our bounds on the SS operators and bipartite correlations for our bounds on the MK operators). We analyze concrete examples in which our bounds are strictly tighter than the known bounds, i.e., lie beneath the previously found constants, thus better characterizing the set of allowed quantum correlations. We interpret the results as complementarity relations between multipartite and local correlations, as well as multipartite and bipartite correlations.

Zhi‐Xiang Jin, Shao-Ming Fei, Cong‐Feng Qiao

Chenxiao Wang, Limin Gao

Abstract 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.