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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Quantifying quantum coherence based on the generalized $\alpha-z-$relative R$\acute{e}$nyi entropy
TL;DR: In this article, a family of coherence quantifiers based on the generalized α-z-relative R$\acute{e}$nyi entropy was proposed, which satisfy all the standard criteria for well-defined measures of coherentness, and include existing coherence measures as special cases.
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Intrinsic degree of coherence of classical and quantum states
TL;DR: In the context of 2D polarization states of light, the degree of polarization P2 is equal to the maximum value of coherence over all possible bases as discussed by the authors, and P2 can be referred to as the intrinsic coherence of a 2D state.
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Coherence Depletion in Quantum Algorithms.
TL;DR: It is shown that the depletion of quantum coherence turns out to be a common phenomenon in quantum algorithms, including Grover's algorithm, Deutsch–Jozsa algorithm, and Shor’s algorithm, which means that coherence depletion can be useful for devising new quantum algorithms in the future.
Journal ArticleDOI
Compact quantum kernel-based binary classifier
TL;DR: This work presents the simplest quantum circuit for constructing a kernel-based binary classifier by generalizing the interference circuit to encode data labels in the relative phases of the quantum state and introducing compact amplitude encoding, which encodes two training data vectors into one quantum register.
Journal ArticleDOI
Impossibility of cloning of quantum coherence
TL;DR: In this paper, it was shown that it is impossible to clone the coherence of an arbitrary quantum state with an ancillary system as machine state, and the impossibility proof also holds when we do not include machine states.
References
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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.