Monogamy of entanglement of formation

Abstract

It is well known that a particle cannot freely share entanglement with two or more particles. This restriction is generally called monogamy. However the formal quantification of such restriction is only known for some measures of entanglement and for two-level systems. The first and broadly known monogamy relation was established by Coffman, Kundu, and Wootters for the square of the concurrence. Since then, it is usually said that the entanglement of formation is not monogamous, as it does not obey the same relation. We show here that despite that, the entanglement of formation cannot be freely shared and therefore should be said to be monogamous. Furthermore, the square of the entanglement of formation does obey the same relation of the squared concurrence, a fact recently noted for three particles and extended here for N particles. Therefore the entanglement of formation is as monogamous as the concurrence. We also numerically study how the entanglement is distributed in pure states of three qubits and the relation between the sum of the bipartite entanglement and the classical correlation.

Entanglement monogamy relations of qubit systems

“…Such monogamy relations are not always satisfied by entanglement measures. Although the concurrence C and entanglement of formation E do not satisfy such monogamy inequality, it has been shown that the squared concurrence C 2 [9,10] and the squared entanglement of formation E 2 [11] do satisfy the monogamy relations. In this paper, we study the general monogamy inequalities satisfied by the αth power of concurrence C α and the αth power of entanglement of formation E α .…”

General monogamy relation of multiqubit systems in terms of squared Rényi-αentanglement

“…However, there exists a kind of three-qubit mixed states which is entangled but without two-qubit concurrence and three-tangle [38], and the similar case also exists in Nqubit systems [39]. Recently, it was indicated that the squared entanglement of formation (SEF) [3] obeys the monogamy relation in multiqubit systems [40][41][42][43][44][45]. In particular, it was which overcomes the flaw of the MoE of SC and can be utilized to detect all multiqubit entanglement.…”

Conditions for monogamy of quantum correlations in multipartite systems

“…The higher power, the graph is nearer to the vertical axis. It has been found that several measures of quantum correlations like squared concurrence [24,25], squared negativity [66][67][68], squared quantum discord [36], global quantum discord [69,70], squared entanglement of formation [71,72], Bell inequality [73][74][75], EPR steering [76,77], contextual inequalities [78,79], etc. exhibit monogamy property.…”