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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Journal ArticleDOI
Secure uniform random-number extraction via incoherent strategies
TL;DR: The maximum secure extraction rate is shown to be equal to the relative entropy of coherence, which clarifies the power of incoherent strategies in random number generation, and can be applied to guarantee the quality of random numbers generated by a quantum random number generator.
Journal ArticleDOI
Endurance of quantum coherence due to particle indistinguishability in noisy quantum networks
Armando Perez-Leija,Diego Guzmán-Silva,Roberto de J. León-Montiel,Markus Gräfe,Matthias Heinrich,Héctor M. Moya-Cessa,Kurt Busch,Alexander Szameit +7 more
TL;DR: In this paper, it was shown that when two indistinguishable noninteracting particles co-propagate through quantum networks affected by non-dissipative noise, the system always evolves into a steady state in which coherences accounting for particle indistinguishabilty perpetually prevail.
Journal ArticleDOI
Coherence of quantum channels
TL;DR: In this paper, the authors investigated the quantum coherence of quantum channels using the Choi-Jamiolkowski isomorphism and found that the allowed region of coherence for a fixed purity is defined by the relation between the coherence and the purity of the channel.
Journal ArticleDOI
Quantum coherence in a quantum heat engine
Yun-Hao Shi,Yun-Hao Shi,Yun-Hao Shi,Hai-Long Shi,Xiao-Hui Wang,Ming-Liang Hu,Si-Yuan Liu,Si-Yuan Liu,Wen-Li Yang,Heng Fan,Heng Fan +10 more
TL;DR: In this article, the authors identify that quantum coherence is a valuable resource in the quantum heat engine, which is designed in a quantum thermodynamic cycle assisted by a quantum Maxwell's demon.
Book ChapterDOI
Resource Theory of Quantum Thermodynamics: Thermal Operations and Second Laws
TL;DR: This chapter shall see in this chapter that thermal interactions can be modelled as a resource theory, and the state transition conditions arising out of such a framework, are referred to as "second laws".
References
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