Global-Local Duality of Energetic Control Cost in Multipartite Quantum Correlated Systems

TL;DR

This paper establishes universal thermodynamic relations for multipartite quantum systems, revealing a duality in control costs and elucidating the role of quantum correlations in energy expenditure during finite-time control tasks.

Contribution

It introduces a global-local duality framework for control costs in multipartite quantum systems, linking quantum correlations to energetic control costs under thermodynamic principles.

Findings

Universal thermodynamic relations for MQCSs are derived.

Quantum correlations influence control costs at finite times.

Numerical validation with multi-qubit systems demonstrates the theory's applicability.

Abstract

Multipartite quantum correlated systems (MQCSs) are widely utilized in diverse quantum information tasks, where their sophisticated control inherently incurs energetic costs. However, the fundamental characteristics of these control costs remain elusive, largely due to the lack of thermodynamic descriptions capable of capturing the full complexities of MQCSs. Here, we uncover universal thermodynamic relations for arbitrary MQCSs weakly coupled to a thermal bath, establishing an intrinsic global-local duality of control costs. Using these relations, we elucidate the exact role of multipartite correlation--a defining quantum feature of MQCSs--in shaping control costs at finite times. We also demonstrate that the relative magnitude between global and local control costs is undetermined, which perplexes the cost management of MQCSs under finite-time controls. Our results are numerically corroborated with applications to experimentally realizable multi-qubit systems undergoing finite-time qubit reset processes.