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
More filters
Majorization requires infinitely many second laws
TL;DR: In this paper , it was shown that for a sufficiently large state space, any family of entropy-like functions constituting a second law is necessarily countably infinite, and an analogous result for a variation of majorization known as thermo-majorization which, in fact, does not require any constraint on the state space provided the equilibrium distribution is not uniform.
Interrelation of nonclassicality features in higher dimensional systems through logical operators
Sooryansh Asthana,V. Ravishankar +1 more
TL;DR: In this paper , the authors generalize the results of Asthana et al. to higher dimensional systems and show that conditions for coherence in logical qudits and logical continuous-variable (cv) systems themselves give rise to conditions for nonlocality and entanglement in their physical constituent qudit and cv systems.
Proceedings ArticleDOI
Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction
TL;DR: In this paper, the authors studied the second-order asymptotics of coherence distillation with and without assistance, and showed that the maximum number of random bits extractable from a given quantum state is precisely equal to the maximum amount of coherent bits that can be distilled from the same state.
Journal ArticleDOI
The Zero-error Entanglement Cost is Highly Non-Additive
TL;DR: In this article, it was shown that the Schmidt number is highly non-multiplicative in the sense that for any integer n, there exists states whose Schmidt number remains constant when taking $n$ copies of the given state.
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.