Discord, quantum knowledge and private communications

TL;DR

This paper reviews how quantum discord, a measure of quantum correlations, is crucial in quantum information tasks like identifying applied unitaries and in quantum cryptography, especially in quantum key distribution and channel capacity.

Contribution

It highlights the role of quantum discord in quantum information processing and cryptography, emphasizing its utility in detecting quantum capabilities and bounding secret key rates.

Findings

Quantum discord detects unitaries applied to quantum systems.

Discord bounds the secret key rates in quantum cryptography.

The secret key capacity of a lossy bosonic channel equals maximum distributed discord.

Abstract

In this brief review, we discuss the role that quantum correlations, as quantified by quantum discord, play in two interesting settings. The first one is discerning which unitaries have been applied on a quantum system, by taking advantage of knowledge regarding its initial configuration. Here discord captures the "quantum" component of this knowledge, useful only when we have access to a quantum memory. In particular, discord can be used to detect whether an untrusted party has certain quantum capabilities. The second setting is quantum cryptography. Here discord represents an important resource for trusted-noise quantum key distribution and also provides a general upper bound for the optimal secret key rates that are achievable by ideal protocols. In particular, the (two-way assisted) secret key capacity of a lossy bosonic channel exactly coincides with the maximum discord that can be distributed between the remote parties at the two ends of the channel.