Monogamy of Quantum Correlations - A Review

Abstract

Monogamy is an intrinsic feature of quantum correlations that gives rise to several interesting quantum characteristics which are not amenable to classical explanations. The monogamy property imposes physical restrictions on unconditional sharability of quantum correlations between the different parts of a multipartite quantum system, and thus has a direct bearing on the cooperative properties of states of multiparty systems, including large many-body systems. On the contrary, a certain party can be maximally classical correlated with an arbitrary number of parties in a multiparty system. In recent years, the monogamy property of quantum correlations has been applied to understand several key aspects of quantum physics, including distribution of quantum resources, security in quantum communication, critical phenomena, and quantum biology. In this chapter, we look at some of the salient developments and applications in quantum physics that have been closely associated with the monogamy of quantum discord, and "discord-like" quantum correlation measures.

Measures and applications of quantum correlations

“…More general (measure-independent) features of QCs in multipartite systems have also been explored, demonstrating in particular that, unlike entanglement measures [320], no measure of QCs beyond entanglement can satisfy a conventional monogamy inequality on all states of three or more parties [74]. However, alternative monogamy constraints that impose trade-offs between QCs and other resources in tripartite systems, such as entanglement, coherence, and local entropies, can be derived [176,177,222,223,85,321,322]. Even more generally, the results reviewed in Section 4.1.1 reveal that QCs beyond entanglement do obey fundamental limits to their shareability, which is another testament to their true quantum nature, as opposed to the case of freely shareable classical correlations.…”

Multipartite entanglement, quantum coherence, and quantum criticality in triangular and Sierpiński fractal lattices

“…Next, we briefly outline the definition of the monogamy of entanglement and the measure of multipartite entanglement in the present study. For an N -qubit system with state space H A1 ⊗ H A2 ⊗ · · · ⊗ H AN , taking the subsystem A 1 as a "node" [34], if the entanglement between the particles A 1 and A 2 , · · · , A N satisfies the inequality…”

“…Since the basic cluster contains seven sites, as shown in Fig. 1(a), we choose the central site (labeled by 1) as the "node" [34], and calculate the seven-partite entanglement τ 1|2,··· ,7 for studying the performances of multipartite entanglement in the QPT. The Hamiltonian of basic cluster can be written as…”

How to Erase Quantum Monogamy?

“…Secondly, recent theoretical advancements have brought to light unexpected structural relationships between the observable aspects of a bipartite singlet state [8,24]. Many interpretations can explain the predictions of quantum theory, but not all of them can account for these subtle nuances, especially in the context of quantum monogamy [25][26][27][28]. In particular, changing the number of variables investigated with an n-quantum system can change the expected rates of coincidence.…”