Energy Cost of Creating Quantum Coherence

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.Comment: 8 pages, Accepted for publication in Physical Review

Universal Coherence-Induced Power Losses of Quantum Heat Engines in Linear Response

We introduce a universal scheme to divide the power output of a periodically driven quantum heat engine into a classical contribution and one stemming solely from quantum coherence. Specializing to Lindblad-dynamics and small driving amplitudes, we derive general upper bounds on both, the coherent and the total power. These constraints imply that, in the linear-response regime, coherence inevitably leads to power losses. To illustrate our general analysis, we explicitly work out the experimentally relevant example of a single-qubit engine.Comment: 7+4 pages, 2 figure