Entropy bounds for quantum processes with initial correlations

TL;DR

This paper derives a generalized entropy bound for quantum processes with initial system-environment correlations, extending key information-theoretic inequalities to non-completely positive dynamics.

Contribution

It introduces a superchannel-based framework to establish entropy bounds valid for correlated quantum systems, generalizing the data processing inequality and Holevo bound.

Findings

Derived a generalized entropy bound for correlated quantum dynamics.

Proved the validity of data processing inequality with initial correlations.

Extended the Holevo bound to systems with system-environment correlations.

Abstract

Quantum technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability of complete-positive trace preserving maps is no longer valid. The departure from complete positivity means many useful bounds, like entropy production, Holevo, and data processing inequality are no longer applicable to such systems. We address these issues by deriving a generalized bound for entropy valid for quantum dynamics with arbitrary system-environment correlations. We employ superchannels, which map quantum operations performed by the experimenter, represented in terms of completely positive maps, to states. Our bound has information-theoretic applications, as it generalizes the data processing inequality and the Holevo bound. We prove that both data processing inequality and the Holevo are valid even when system is correlated with the environment.