Related papers: Coherence as entropy increment for Tsallis and Ren…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
Uncertainty relations for more than two observables have found use in quantum information, though commonly known relations pertain to a pair of observables. We present novel uncertainty and certainty relations of state-independent form for…
We prove that the inequality used recently by Wilk and W{\l}odarczyk [Phys. Rev. A {\bf 79}, 062108 (2009)] to find a better lower bound in the uncertainty relations for the R\'enyi entropies is invalid. Thus, the problem of improving the…
Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a…
In this work, we analyze alternative effective sample size (ESS) metrics for importance sampling algorithms, and discuss a possible extended range of applications. We show the relationship between the ESS expressions used in the literature…
We studied the Sharma-Mittal relative entropy and showed that its physical meaning is the free energy difference between the off-equilibrium and equilibrium distributions. Unfortunately, Sharma-Mittal relative entropy may acquire this…
The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation.…
It is shown that Lesche's conclusions on instability of the Renyi entropy are the same for the Tsallis entropy, as well. Moreover, they are unjustified for both entropies.
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak…
Some preliminary evidence suggests the conjecture that the collective behaviour of systems having long-range interactions may be described more effectively by the Tsallis rather than by the Boltzmann/Gibbs/Shannon entropy. To this end, we…
The pseudo-additive relation that the Tsallis entropy satisfies has nothing whatsoever to do with the super- and sub- additivity properties of the entropy. The latter properties, like concavity and convexity, are couched in geometric…
The study of quantum correlations in High-dimensional bipartite systems is crucial for the development of quantum computing. We propose relative entropy as a distance measure of correlations may be measured by means of the distance from the…
The relative entropy of a correlated state and an uncorrelated reference state is a reasonable measure for the degree of correlations. A key question is however which uncorrelated state to compare to. The relative entropy becomes minimal…
We investigate the coherence measures induced by fidelity and trace norm, based on the recent proposed coherence quantification in [Phys. Rev. Lett. 113, 140401, 2014]. We show that the fidelity of coherence does not in general satisfy the…
We present a method for improving measurements of the entanglement R\'enyi entropies in quantum Monte Carlo simulations by relating them with measurements of participation R\'enyi entropies. Exploiting the capability of building improved…
Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of…
Quantum coherence is the most distinguished signature of quantum mechanics, also recognized to be an essential resource for many promising quantum technologies, playing a central role in phenomena related to quantum information science,…
Quantum coherence is the most fundamental feature of quantum mechanics. The usual understanding of it depends on the choice of the basis, that is, the coherence of the same quantum state is different within different reference framework. To…
We study partial coherence and its connections with entanglement. First, we provide a sufficient and necessary condition for bipartite pure state transformation under partial incoherent operations: A bipartite pure state can be transformed…