# Quantifying the Unitary Generation of Coherence From Thermal Quantum Systems

## TL;DR

This paper investigates how to optimally generate quantum coherence from thermal states using controllable unitaries, revealing energy distribution patterns and the impact of work constraints on coherence.

## Contribution

It introduces a control framework for maximizing coherence from thermal states, analyzing energy distributions and the effects of work constraints on the process.

## Key findings

- Maximum coherence corresponds to micro-canonical energy distribution.
- Generating coherence requires external work, with constraints leading to canonical distributions.
- Optimal control can avoid local traps and achieve global maxima with appropriate energy constraints.

## Abstract

The unitary generation of coherence from an incoherent thermal state is investigated. We consider a completely controllable Hamiltonian allowing to generate all possible unitary transformations. Optimizing the unitary control to achieve maximum coherence leads to a micro-canonical energy distribution on the diagonal energy representation. We demonstrate such a control scenario starting from a Hamiltonian utilizing optimal control theory for unitary targets. Generating coherence from an incoherent initial state always costs external work. By constraining the amount of work invested by the control, maximum coherence leads to a canonical energy population distribution. When the optimization procedure constrains the final energy too tightly local suboptimal traps are found. The global optimum is obtained when a small Lagrange multiplier is employed to constrain the final energy. Finally, we explore constraining the generated coherence to be close to the diagonal in the energy representation.