Exploring multipartite quantum correlations with the square of quantum discord

Abstract

We explore the quantum correlation distribution in multipartite quantum states based on the square of quantum discord (SQD). For tripartite quantum systems, we derive the necessary and sufficient condition for the SQD to satisfy the monogamy relation. Particularly, we prove that the SQD is monogamous for three-qubit pure states, based on which a genuine tripartite quantum correlation measure is introduced. In addition, we also address the quantum correlation distributions in four-qubit pure states. As an example, we investigate multipartite quantum correlations in the dynamical evolution of multipartite cavity-reservoir systems.

Monogamy of entanglement of formation

“…[5] or in Ref. [8], we reproduce their arguments here for the general case. We start with the fact that the E 2 F is a monotonic function of C 2 and, using the CKW monogamy for N qubits, we have…”

“…Since then, it is usually said that EF is not monogamous. It is curious that the authors analyzed EF and not its square, since they were working with C 2 and not C. In fact it is easy to show that E 2 F does obey the monogamy relation for qubits, and this fact was first noticed by Bai et al [8]. Their proof is for 3 qubits, but their argument is equally valid for N qubits.…”

“…This monogamous relation has also been studied for other entanglement measures [4,7,8] and also for the discord [9][10][11][12]. It is well known that the entanglement of formation, when not squared, does not obey the inequality given by Eq.…”

“…In fact, we numerically found an upper bound for E 12 + E 13 using the entanglement of formation, which is considerably smaller than 2. Besides, very recently it was shown by Bai et al [8] that, when squared, EF does satisfy a monogamy relation for three-qubit systems like the concurrence. We also generalize this result for N qubits.…”

Quantum Correlations in Multipartite Quantum Systems

“…And actually not even the concurrence or the entanglement of formation obey the CKW inequality, but only their squares. And it was later realized that the square of discord does obey the CKW inequality [29], being in this sense as monogamous as entanglement. In fact there is a stronger relation between entanglement of formation and discord for three qubits.…”