Characterizing entanglement using quantum discord over state extensions

TL;DR

This paper establishes a fundamental link between quantum discord and entanglement, showing that entanglement can be viewed as an irreducible component of discord over state extensions, with operational and quantitative implications.

Contribution

It introduces a framework connecting quantum discord and entanglement via Bures distance and relative entropy, revealing entanglement as a primitive aspect of discord.

Findings

Bures distance of discord over state extensions equals Bures distance of entanglement.

Entanglement measure by Devi and Rajagopal is equivalent to relative entropy of entanglement.

Provides quantifications of entanglement based on discord measures.

Abstract

We propose a framework to characterize entanglement with quantum discord, both asymmetric and symmetric, over state extensions. In particular, we show that the minimal Bures distance of discord over state extensions is equivalent to Bures distance of entanglement. This equivalence places quantum discord at a more primitive position than entanglement conceptually in the sense that entanglement can be interpreted as an irreducible part of discord over all state extensions. Based on this equivalence, we also offer an operational meaning of Bures distance of entanglement by connecting it to quantum state discriminations. Moreover, for the relative entropy part, we prove that the entanglement measure introduced by Devi and Rajagopal [A. R. U. Devi and A. K. Rajagopal, Phys. Rev. Lett. 100, 140502 (2008)] is actually equivalent to the relative entropy of entanglement. We also provide several quantifications of entanglement based on discord measures.