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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Quantum resource theories
Eric Chitambar,Gilad Gour +1 more
TL;DR: This paper introduced a new development in theoretical quantum physics, the ''resource-theoretic'' point of view, which aims to be closely linked to experiment, and to state exactly what result you can hope to achieve for what expenditure of effort in the laboratory.
Journal ArticleDOI
Entropic uncertainty relations and their applications
TL;DR: This review surveys entropic uncertainty relations that capture Heisenberg’s idea that the results of incompatible measurements are impossible to predict, covering both finite- and infinite-dimensional measurements.
Journal ArticleDOI
Robustness of Coherence: An Operational and Observable Measure of Quantum Coherence.
Carmine Napoli,Carmine Napoli,Thomas R. Bromley,Marco Cianciaruso,Marco Cianciaruso,Marco Piani,Nathaniel Johnston,Gerardo Adesso +7 more
TL;DR: The robustness of coherence is defined and proven to be a full monotone in the context of the recently introduced resource theories of quantum coherence, and the measure is shown to be observable.
Journal ArticleDOI
Converting Coherence to Quantum Correlations
TL;DR: It is shown how the interplay between quantum coherence consumption and creation of quantum discord works in the preparation of multipartite quantum correlated states and in the model of deterministic quantum computation with one qubit.
Journal ArticleDOI
Quantum coherence and geometric quantum discord
TL;DR: This aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states.
References
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Book
Stochasticity and Partial Order: Doubly Stochastic Maps and Unitary Mixing
A. Uhlmann,P.M. Alberti +1 more
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TL;DR: The entanglement cost of several families of bipartite mixed states, including arbitrary mixtures of two Bell states are computed by developing a technique that allows us to ascertain the additivity of theEntanglement of formation for any state supported on specific subspaces.
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Continuity bounds for entanglement
TL;DR: In this article, the authors quantified the continuity properties of entanglement and studied how much the quantum state of a bipartite system can change if we change the entangled quantum state just a little.