Internal Entanglement and External Correlations of Any Form Limit Each Other

Abstract

We show a relation between entanglement and correlations of any form. The internal entanglement of a bipartite system, and its correlations with another system, limit each other. A measure of correlations, of any nature, cannot increase under local operations. Examples are the entanglement monotones, the mutual information that quantifies total correlations, and the Henderson-Vedral measure of classical correlations. External correlations, evaluated by such a measure, set a tight upper bound on the internal entanglement that decreases as they increase, and so does quantum discord.

Realization of the tradeoff between internal and external entanglement

“…Furthermore, our experiment will be greatly helpful for further research on the other monogamy relations in multipartite systems. For instance, one can demonstrate the inequality between local coherence and entanglement [48,61] and the inequality between intraparticle entanglement and external correlations [51].…”

“…Many familiar entanglement monotones satisfy monogamy inequalities of the form of Eq. (8) [51], but determining explicitly the corresponding function g may not be always possible. Now we present another case for which this can be achieved.…”

“…On the other hand, many experimental results on entanglement and nonlocality have also been reported [44,45], including entanglement monogamy in experiments [46,47]. Recently, new kinds of monogamy relations have been derived by Camalet [48][49][50][51], i.e., internal entanglement (or local quantum resource) and external entanglement have a tradeoff. The usually discussed entanglement monogamy inequalities in Refs.…”

Existence of maximally correlated states

“…First, for pure bipartite states, the only form of correlation is entanglement [20], and so maximally entangled states may be maximally correlated in some sense in this case. Second, it has been shown that the internal entanglement of a bipartite system is constrained by its total correlations with another system [19]. The found upper bound always decreases as the correlations increase, but, depending on the measure of correlations used, the internal entanglement necessarily vanishes for maximal correlations or not.…”

Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems

“…Moreover, Koashi and Winter proved that the one-way distillable entanglement and squashed entanglement satisfy monogamy inequalities for any tripartite systems of ar-bitrary dimension [25]. Recently, some different kinds of monogamy relations [26][27][28][29][30][31][32] were introduced. The monogamy relations involving other measures of quantum correlations have also been reported [33][34][35][36][37][38][39].…”