Quantum Discord Bounds the Amount of Distributed Entanglement

Abstract

The ability to distribute quantum entanglement is a prerequisite for many fundamental tests of quantum theory and numerous quantum information protocols. Two distant parties can increase the amount of entanglement between them by means of quantum communication encoded in a carrier that is sent from one party to the other. Intriguingly, entanglement can be increased even when the exchanged carrier is not entangled with the parties. However, in light of the defining property of entanglement stating that it cannot increase under classical communication, the carrier must be quantum. Here we show that, in general, the increase of relative entropy of entanglement between two remote parties is bounded by the amount of nonclassical correlations of the carrier with the parties as quantified by the relative entropy of discord. We study implications of this bound, provide new examples of entanglement distribution via unentangled states, and put further limits on this phenomenon.

Measures and applications of quantum correlations

“…In fact, whenever QCs are not present, the transmission of the carrier particle C effectively reduces to classical communication. Examples of states ρ ABC were given in [222] for when this bound is tight, and it was argued in [223] that entanglement distribution with separable states may be more efficient than using entangled carriers if local generation of entanglement at the sender laboratory is expensive.…”

Excessive distribution of quantum entanglement

“…The first example of a pure state that does not satisfy inequality (15) has been encountered for d A = 4 with B and C both being qubits. For instance, for state…”

“…The left inequality is obtained from E AC:B = E AC:BD , as initially Bob's ancilla is completely uncorrelated, and using E A:BD ≤ E AC:BD , due to tracing out one subsystem. The case of EB channels clearly illustrates that, although communicated quantum discord is necessary for entanglement gain [14,15], it is not a tight bound to entanglement gain in every distribution protocol [9]. The state resulting from EB channels can possess some discord as measured on the ancilla, but this can be thought of as being locally created by a device in Bob's laboratory, which in fact is fed with purely classical communication.…”

“…On the other hand, it generated great curiosity on what really limits the distribution, if not the carried entanglement. In [14,15] it has been shown that quantum discord is a necessary condition for a successful distribution, providing an upper bound to the amount of entanglement generated. However, the presence of discord in the carrier is not a sufficient condition, and e.g.…”

Multipartite quantum and classical correlations in symmetric n-qubit mixed states

“…The interest around such a quantumness quantifier is justified considering the fact that there are examples in mixed-state quantum computation where it appears clear that entanglement in not the only meaningful indicator [4][5][6]. Even if the role of discord in quantum computation has not yet been fully clarified, there are many contexts where its use has been productive [7][8][9][10].…”