Conservation law for distributed entanglement of formation and quantum discord

TL;DR

This paper establishes a conservation law linking entanglement of formation and quantum discord in tripartite quantum systems, revealing how quantum correlations are redistributed during quantum processes and impacting our understanding of quantum computation.

Contribution

It introduces a conservation relation between EOF and QD based on monogamy, extending it to bipartite systems with environments, and applies it to quantum computing and entropy inequalities.

Findings

EOF and QD obey a conservation relation in tripartite systems

Quantum correlations can be redistributed in quantum computation

Stronger form of strong subadditivity derived for mixed states

Abstract

We present a direct relation, based upon a monogamic principle, between entanglement of formation (EOF) and quantum discord (QD), showing how they are distributed in an arbitrary tripartite pure system. By extending it to a paradigmatic situation of a bipartite system coupled to an environment, we demonstrate that the EOF and the QD obey a conservation relation. By means of this relation we show that in the deterministic quantum computer with one pure qubit the protocol has the ability to rearrange the EOF and the QD, which implies that quantum computation can be understood on a different basis as a coherent dynamics where quantum correlations are distributed between the qubits of the computer. Furthermore, for a tripartite mixed state we show that the balance between distributed EOF and QD results in a stronger version of the strong subadditivity of entropy.