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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Using and reusing coherence to realize quantum processes
María García Díaz,Kun Fang,Xin Wang,Matteo Rosati,Michalis Skotiniotis,John Calsamiglia,Andreas Winter,Andreas Winter +7 more
TL;DR: It is found that in general a quantum channel can be implemented without employing a maximally coherent resource state, and it is proved that every pure coherent state in dimension larger than 2 turns out to be a valuable resource to implement some coherent unitary channel.
Journal ArticleDOI
No-Go Theorems for Quantum Resource Purification.
Kun Fang,Kun Fang,Zi-Wen Liu +2 more
TL;DR: It is proved fundamental limitations on how effectively generic noisy resources can be purified enforced by the laws of quantum mechanics, which universally apply to any reasonable kind of quantum resource.
Journal ArticleDOI
Operational relevance of resource theories of quantum measurements
Michał Oszmaniec,Tanmoy Biswas +1 more
TL;DR: It is proved that every resource measurement offers advantage for some quantum state discrimination task, and an operational interpretation of robustness is given, which quantifies the minimal amount of noise that must be added to a measurement to make it free.
Posted ContentDOI
Resource theories of quantum channels and the universal role of resource erasure
Zi-Wen Liu,Andreas Winter +1 more
TL;DR: In this article, the authors studied resource theories of quantum channels, i.e. of the dynamics that quantum systems undergo by completely positive maps, in abstracto: resources are in principle all maps from one quantum system to another, but some maps are deemed free.
Journal ArticleDOI
Experimental Cyclic Interconversion between Coherence and Quantum Correlations
Kang-Da Wu,Zhibo Hou,Yuan-Yuan Zhao,Guo-Yong Xiang,Chuan-Feng Li,Guang-Can Guo,Jiajun Ma,Qiongyi He,Jayne Thompson,Mile Gu,Mile Gu +10 more
TL;DR: This experiment highlights the connection between nonclassicality of correlations and non classicality within local quantum systems and provides potential flexibilities in exploiting one resource to perform tasks normally associated with the other.
References
More filters
Book
Elements of information theory
Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Journal ArticleDOI
Entanglement of Formation of an Arbitrary State of Two Qubits
TL;DR: In this article, an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix was conjectured.
Journal ArticleDOI
Quantum entanglement
TL;DR: In this article, the basic aspects of entanglement including its characterization, detection, distillation, and quantification are discussed, and a basic role of entonglement in quantum communication within distant labs paradigm is discussed.
Book
Inequalities: Theory of Majorization and Its Applications
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.
Journal ArticleDOI
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.