Energy Cost of Creating Quantum Coherence

TL;DR

This paper investigates the maximum quantum coherence achievable from thermal states using limited energy, exploring the trade-offs with total correlations and providing explicit optimal unitaries.

Contribution

It derives the maximal coherence achievable under energy constraints and compares it with total correlation creation, revealing fundamental trade-offs.

Findings

Maximal coherence can be explicitly achieved with specific unitaries.

Total correlation creation is bounded by the amount of coherence when energy is limited.

No unitary can simultaneously maximize coherence and correlation with limited energy.

Abstract

We consider the physical situations where the resource theories of coherence and thermodynamics play competing roles. In particular, we study the creation of quantum coherence using unitary operations with limited thermodynamic resources. We first find the maximal coherence that can be created under unitary operations starting from a thermal state and find explicitly the unitary transformation that creates the maximal coherence. Since coherence is created by unitary operations starting from a thermal state, it requires some amount of energy. This motivates us to explore the trade-off between the amount of coherence that can be created and the energy cost of the unitary process. We find the maximal achievable coherence under the constraint on the available energy. Additionally, we compare the maximal coherence and the maximal total correlation that can be created under unitary transformations with the same available energy at our disposal. We find that when maximal coherence is created with limited energy, the total correlation created in the process is upper bounded by the maximal coherence and vice versa. For two qubit systems we show that there does not exist any unitary transformation that creates maximal coherence and maximal total correlation simultaneously with a limited energy cost.