Operational Resource Theory of Coherence.
By Andreas J. Winter, Dong Yang. Physical Review Letters, 2015
807 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Cognitive Neuroscience
View Paper: https://www.semanticscholar.org/paper/881eacae4e383019c61be48c15a91b84f25af267
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Quantum processes which do not use coherence (2015, background): “[6] Andreas Winter and Dong Yang, “Operational resource theory of coherence,” Phys.”
- Entropic uncertainty relations and their applications (2015, neutral): “There are a variety of coherence measures, but one in particular has an operational meaning in terms of the number of distillable maximally coherent states (Winter and Yang, 2016), Φ(Z, ρ) := D ( ρ ∥∥∥∥∥∑ z |Zz〉〈Zz|ρ|Zz〉〈Zz| ) , (347) the relative entropy of coherence.”
- Quantum coherence and geometric quantum discord (2017, background): “…= C ε SIO(ρ) = C ε 0(ρ), (360) and in the asymptotic limit, the ε-smoothed coherence equivalents either to the relative entropy of coherence (Baumgratz et al., 2014) or to the coherence of formation (Winter and Yang, 2016), i.e., C∞MIO(ρ) = C ∞ DIO(ρ) = Cr(ρ), C∞IO(ρ) = C ∞ SIO(ρ) = C f (ρ).”
- Coherence effects in the performance of the quantum Otto heat engine (2018, background): “where ε (·) = ∑ n Πn (·) Πn is the full dephasing map and C (ρ) = S (ε (ρ)) − S (ρ) is the relative entropy of coherence (in the reference state basis) [12–16].”
- Operational one-to-one mapping between coherence and entanglement measures (2017, background): “sense that KnρK † n is incoherent whenever ρ is [3,23,28,29].”