Discord and quantum computational resources

TL;DR

This paper investigates the role of quantum discord in quantum algorithms, revealing that manipulating discord involves costs in entanglement and communication, and introduces K-discord as a new resource constraint.

Contribution

It introduces K-discord as a new measure to understand the resource requirements for operations on discordant states in quantum computing.

Findings

Manipulating discord incurs entanglement and communication costs.

Changing discord reduces total correlations.

K-discord constrains operations without entanglement.

Abstract

Discordant states appear in a large number of quantum phenomena and seem to be a good indicator of divergence from classicality. While there is evidence that they are essential for a quantum algorithm to have an advantage over a classical one, their precise role is unclear. We examine the role of discord in quantum algorithms using the paradigmatic framework of `restricted distributed quantum gates' and show that manipulating discordant states using local operations has an associated cost in terms of entanglement and communication resources. Changing discord reduces the total correlations and reversible operations on discordant states usually require non-local resources. Discord alone is, however, not enough to determine the need for entanglement. A more general type of similar quantities, which we call K-discord, is introduced as a further constraint on the kinds of operations that can be performed without entanglement resources.