相关论文: Continuity bounds on the quantum relative entropy
Gaussian distribution of a quantum state with continuous spectrum is known to maximize the Shannon entropy at a fixed variance. Applying it to a pair of canonically conjugate quantum observables $\hat x$ and $\hat p$, quantum entropic…
We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…
The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate…
Given an arbitrary quantum state ($\sigma$), we obtain an explicit construction of a state $\rho^*_\varepsilon(\sigma)$ (resp. $\rho_{*,\varepsilon}(\sigma)$) which has the maximum (resp. minimum) entropy among all states which lie in a…
The most fundamental properties of quantum entropy are derived by considering the union of two ensembles. We discuss the limits these properties put on an entropy measure and obtain that they uniquely determine the form of the entropy…
We give a pedagogical introduction to quantum discord. We the discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
With growing success in experimental implementations it is critical to identify a "gold standard" for quantum information processing, a single measure of distance that can be used to compare and contrast different experiments. We enumerate…
Combining gravity with quantum theory is still work in progress. On the one hand, classical gravity, is the geometry of space-time determined by the energy-momentum tensor of matter and the resulting nonlinear equations; on the other hand,…
Understanding the limitations imposed by noise on current and next-generation quantum devices is a crucial step towards demonstrating practical quantum advantage. In this work, we investigate the accumulation of entropy density as a…
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…
Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can~there be some trade-off relation between the…
An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…
Quantum processes can be divided into two categories: unitary and non-unitary ones. For a given quantum process, we can define a \textit{degree of the unitarity (DU)} of this process to be the fidelity between it and its closest unitary…
New upper bounds on the relative entropy are derived as a function of the total variation distance. One bound refines an inequality by Verd\'{u} for general probability measures. A second bound improves the tightness of an inequality by…
In this work we study the properties of an purification-based entropic metric for measuring the distance between both quantum states and quantum processes. This metric is defined as the square root of the entropy of the average of two…
Entanglement is not only the resource that fuels many quantum technologies but also plays a key role for some of the most profound open questions of fundamental physics. Experiments controlling quantum systems at the single quantum level…
We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is…
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…