Related papers: Upper continuity bound on the quantum quasi-relati…
When particles interact via two-body short-range central potential wells, binding can occur for some critical values of the coupling constants. Using the envelope theory, upper bounds for critical coupling constants are computed for quantum…
Nonlocality and entanglement are not only the fundamental characteristics of quantum mechanics but also important resources for quantum information and computation applications. Exploiting the quantitative relationship between the two…
Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$…
For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from…
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…
Elaborating on a previous work by Marolf et al, we relate some exact results in quantum field theory and statistical mechanics to the Bekenstein universal bound on entropy. Specifically, we consider the relative entropy between the vacuum…
The nonextensive entropic measure proposed by Tsallis introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On…
Compact expressions for the average subentropy and coherence are obtained for random mixed states that are generated via various probability measures. Surprisingly, our results show that the average subentropy of random mixed states…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
We prove a tight uniform continuity bound for Arimoto's version of the conditional $\alpha$-R\'enyi entropy, for the range $\alpha \in [0, 1)$. This definition of the conditional R\'enyi entropy is the most natural one among the multiple…
We study the entanglement of a pure state of a composite quantum system consisting of several subsystems with $d$ levels each. It can be described by the R\'enyi-Ingarden-Urbanik entropy $S_q$ of a decomposition of the state in a product…
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…
We investigate entanglement measures in the infinite-dimensional regime. First, we discuss the peculiarities that may occur if the Hilbert space of a bi-partite system is infinite-dimensional, most notably the fact that the set of states…
We define and analyze measures of correlations for bipartite states based on trace distance. For Bell diagonal states of two qubits, in addition to the known expression for quantum correlations using this metric, we provide analytic…
The trace distance between two quantum states, $\rho$ and $\sigma$, is an operationally meaningful quantity in quantum information theory. However, in general it is difficult to compute, involving the diagonalization of $\rho - \sigma$. In…
We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference…
Uncertainty relations emerging from the Tsallis entropy are derived and discussed. In particular we found a positively defined function that saturates the so called entropic inequalities for entropies characterizing the physical states…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…