Max- relative entropy of coherence: an operational coherence measure

The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of max-relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher probability of successfully discriminating subchannels than that of all incoherent states. This advantage of coherent states in subchannel discrimination can be exactly characterized by the max-relative entropy of coherence. By introducing suitable smooth max-relative entropy of coherence, we prove that the smooth max-relative entropy of coherence provides a lower bound of one-shot coherence cost, and the max-relative entropy of coherence is equivalent to the relative entropy of coherence in asymptotic limit. Similar to max-relative entropy of coherence, min-relative entropy of coherence has also been investigated. We show that the min-relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in asymptotic limit the min-relative entropy of coherence is equivalent to the relative entropy of coherence.Comment: v2. 5+6.5 pages, no figure, close to the published version. v1. 5.5+6 pages, no figur

The Fidelity and Trace Norm Distances for Quantifying Coherence

We investigate the coherence measures induced by fidelity and trace norm, based on the recent proposed coherence quantification in [Phys. Rev. Lett. 113, 140401, 2014]. We show that the fidelity of coherence does not in general satisfy the monotonicity requirement as a measure of coherence under the subselection of measurements condition. We find that the trace norm of coherence can act as a measure of coherence for qubit case and some special class of qutrits.Comment: 4 pages, 1 figure

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