Monogamy of Quantum Entanglement

Abstract

Unlike classical correlation, quantum entanglement cannot be freely shared among many parties. This restricted shareability of entanglement among multi-party systems is known as monogamy of entanglement, which is one of the most fundamental properties of entanglement. Here, we summarize recent theoretical progress in the field of monogamy of entanglement. We firstly review the standard CKW-type monogamy inequalities in terms of various entanglement measures. In particular, the squashed entanglement and one-way distillable entanglement are monogamous for arbitrary dimensional systems. We then introduce some generalized version of monogamy inequalities which extend and sharpen the traditional ones. We also consider the dual polygamy inequalities for multi-party systems. Moreover, we present two new definitions to define monogamy of entanglement. Finally, some challenges and future directions for monogamy of entanglement are highlighted.

Virtual Excitations and Entanglement Dynamics and Polygamy in Three Ultra‐Strongly Coupled Systems

“…The present choice will be justified later, when the interconnection between excitations and entanglement is addressed. Similarly, we define the excitation in the partition $$(k|lm)$$ by $$$$\begin{eqnarray} N_{k|lm}&=& \sqrt {\langle N_{k} \rangle N_{l|m} } \end{eqnarray}$$$$The excitations will be polygamous [ 51 ] if they satisfy the following triangular inequality $$$$\begin{eqnarray} N_{k|lm}\le N_{k|l}+N_{k|m} \end{eqnarray}$$$$These inequalities constrain the generation and extinction of excitations. This finding can be used to consider virtual excitations as a kind of quantum correlation.…”

“…The present choice will be justified later, when the interconnection between excitations and entanglement is addressed. Similarly, we define the excitation in the partition (k|lm) by The excitations will be polygamous [51] if they satisfy the following triangular inequality…”

Protocol for Nonlinear State Discrimination in Rotating Condensate

“…This is achieved by making $$n$$ large, interactions weak, and by preserving permutation symmetry. In this limit entanglement monogamy [ 25,26 ] bounds the pairwise concurrence to zero, and the BEC is exactly described by a nonlinear Schrödinger equation (the Gross–Pitaevskii equation [ 27,28 ] ), enabling novel dynamics. [ 10–12,29–36 ] The theory is developed in a large $$n$$ limit with a rigorous bound on the error resulting from the mean field approximation.…”

On monogamy and polygamy relations of multipartite systems

“…where  is a bipartite entanglement measure, A A r . The monogamy relation was generalized to multiqubit quantum systems, high-dimensional quantum systems in general settings [3][4][5][6][7][8][9][10][11][12][13]. The first polygamy relation of entanglement was established in [14] for some threequbit system as the inequality…”