Operational Resource Theory of Coherence.
TLDR
An operational theory of coherence (or of superposition) in quantum systems is established, by focusing on the optimal rate of performance of certain tasks, by demonstrating that the coherence theory is generically an irreversible theory by a simple criterion that completely characterizes all reversible states.Abstract:
We establish an operational theory of coherence (or of superposition) in quantum systems, by focusing on the optimal rate of performance of certain tasks. Namely, we introduce the two basic concepts-"coherence distillation" and "coherence cost"-in the processing quantum states under so-called incoherent operations [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. We, then, show that, in the asymptotic limit of many copies of a state, both are given by simple single-letter formulas: the distillable coherence is given by the relative entropy of coherence (in other words, we give the relative entropy of coherence its operational interpretation), and the coherence cost by the coherence of formation, which is an optimization over convex decompositions of the state. An immediate corollary is that there exists no bound coherent state in the sense that one would need to consume coherence to create the state, but no coherence could be distilled from it. Further, we demonstrate that the coherence theory is generically an irreversible theory by a simple criterion that completely characterizes all reversible states.read more
Citations
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Asymmetry and coherence weight of quantum states
TL;DR: In this article, the authors introduce the notion of asymmetry weight, an operationally motivated quantifier in the resource theory of asymmetric quantifiers, and study the convexity and monotonicity properties of the asymmetry quantifier.
Journal ArticleDOI
Hierarchy of the nonlocal advantage of quantum coherence and Bell nonlocality
TL;DR: In this article, a hierarchy between the nonlocal advantage of quantum coherence (NAQC) and Bell non-locality is established for two-qubit states with diagonal correlation matrix, and the NAQC created on one qubit by local measurement on another qubit captures quantum correlation which is stronger than Bell nonlocality.
Journal ArticleDOI
Relative submajorization and its use in quantum resource theories
TL;DR: Relative submajorization as mentioned in this paper is a generalization of relative majorization and has many applications to the resource theories of thermodynamics, bipartite entanglement, and quantum coherence.
Journal ArticleDOI
Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
TL;DR: A systematic framework to study linear bosonic non-Gaussian channels of continuous-variable systems by extending quantum-limited Gaussian channels with photon addition applied to the environment state in the Stinespring dilation of these channels is presented.
Journal ArticleDOI
Coherence measure in terms of the Tsallis relative α entropy.
Haiqing Zhao,Chang-shui Yu +1 more
TL;DR: A family of coherence quantifiers which are closely related to the Tsallis relative α entropy are established and it is proved that this family of quantifiers satisfy all the standard criteria and particularly cover several typical coherence measures.
References
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TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
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Quantifying Coherence
TL;DR: In this article, a rigorous framework for quantification of coherence and identification of intuitive and easily computable measures for coherence has been proposed by adopting coherence as a physical resource.