No abstract

The operational characterization of quantum coherence is the cornerstone in the development of the resource theory of coherence. We introduce a new coherence quantifier based on maximum relative entropy. We prove that the maximum 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 the maximum 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 maximum relative entropy of coherence. By introducing a suitable smooth maximum relative entropy of coherence, we prove that the smooth maximum relative entropy of coherence provides a lower bound of one-shot coherence cost, and the maximum relative entropy of coherence is equivalent to the relative entropy of coherence in the asymptotic limit. Similar to the maximum relative entropy of coherence, the minimum relative entropy of coherence has also been investigated. We show that the minimum relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in the asymptotic limit the minimum relative entropy of coherence is equivalent to the relative entropy of coherence.

Quantum coherence is a basic feature of quantum physics. Combined with tensor product structure of state space, it gives rise to the novel concepts such as entanglement and quantum correlations, which play a crucial role in quantum information processing tasks. However, quantum correlations, especially entanglement, are fragile under decoherence. In this context, very few investigations have touched on the production of quantum coherence by quantum operations. In this paper, we study cohering power -- the ability of quantum operations to produce coherence. First, we provide an operational interpretation of cohering power. Then, we decompose a generic quantum operation into three basic operations, namely, unitary, appending and dismissal operations, and show that the cohering power of any quantum operation is upper bounded by the corresponding unitary operation. Furthermore, we compare cohering power and generalized cohering power of quantum operations for different measures of coherence.Comment: 11pages, close to the published versio

We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in Lu et al. [X. M. Lu, S. Luo, and C. H. Oh, Phys Rev. A 86, 022342 (2012)], we show that the presence of quantum correlation can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord for pure quantum states.

Catalytic coherence transformations allow the otherwise impossible state transformations using only incoherent operations with the aid of an auxiliary system with finite coherence which is not being consumed in anyway. Here we find the necessary and sufficient conditions for the deterministic and stochastic catalytic coherence transformations between pair of pure quantum states. In particular, we show that the simultaneous decrease of a family of Rényi entropies of the diagonal parts of the states under consideration are necessary and sufficient conditions for the deterministic catalytic coherence transformations. Similarly, for stochastic catalytic coherence transformations we find the necessary and sufficient conditions for achieving higher optimal probability of conversion. We, thus, completely characterize the coherence transformations amongst pure quantum states under incoherent operations. We give numerous examples to elaborate our results. We also explore the possibility of the same system acting as a catalyst for itself and find that indeed self catalysis is possible. Further, for the cases where no catalytic coherence transformation is possible we provide entanglement assisted coherence transformations and find the necessary and sufficient conditions for such transformations.