Verifying the quantumness of bipartite correlations

TL;DR

This paper proves a fundamental limitation in detecting entanglement, showing that any measurement distinguishing entangled states from separable ones requires full state information, except for quantum discord.

Contribution

It establishes that entanglement detection generally demands complete state tomography, except for quantum discord, which can be identified with less information.

Findings

Entanglement detection requires full state tomography in general.

Quantum discord can be identified without full state tomography.

Other correlations like NPT and classical correlations need full state information.

Abstract

Entanglement is at the heart of most quantum information tasks, and therefore considerable effort has been made to find methods of deciding the entanglement content of a given bipartite quantum state. Here, we prove a fundamental limitation to deciding if an unknown state is entangled or not: we show that any quantum measurement which can answer this question necessarily gives enough information to identify the state completely. Therefore, only prior information regarding the state can make entanglement detection less expensive than full state tomography in terms of the demanded quantum resources. We also extend our treatment to other classes of correlated states by considering the problem of deciding if a state is NPT, discordant, or fully classically correlated. Remarkably, only the question related to quantum discord can be answered without resorting to full state tomography.