Related papers: Quantum Skew Divergence
We present mathematical techniques for addressing two closely related questions in quantum communication theory. In particular, we give a statistically motivated derivation of the Bures-Uhlmann measure of distinguishability for density…
The Holevo quantity provides an upper bound for the mutual information between the sender of a classical message encoded in quantum carriers and the receiver. Applying the strong sub-additivity of entropy we prove that the Holevo quantity…
Change of measure inequalities translate divergences between probability measures into explicit bounds on event probabilities, and play an important role in deriving probabilistic guarantees in learning theory, information theory, and…
We summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with…
Distinguishability is fundamental to information theory and extends naturally to quantum systems. While quantum state discrimination is well understood, quantum channel discrimination remains challenging due to the dynamic nature of…
Schur-Weyl duality is a powerful tool in representation theory which has many applications to quantum information theory. We provide a generalization of this duality and demonstrate some of its applications. In particular, we use it to…
Uncertainty principle is one of the most essential features in quantum mechanics and plays profound roles in quantum information processing. We establish tighter summation form uncertainty relations based on metric-adjusted skew information…
Here we focus on the measurement induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the…
In this article we study relationship between three measures of distinguishability of quantum states called as divergence, relative entropy and the substate property.
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed…
We shall give a new Schr\"odinger type uncertainty relation for a quantity representing a quantum uncertainty, introduced by S.Luo in \cite{Luo1}. Our result improves the Heisenberg uncertainty relation shown in \cite{Luo1} for a mixed…
In this paper we intend to give a comprehensive approach of functional inequalities for diffusion processes under some "curvature" assumptions. Our notion of curvature coincides with the usual $\Gamma_2$ curvature of Bakry and Emery in the…
The paper by Leiva et al. (2010) introduced a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum-Saunders distribution associated with this distribution. In this…
This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
We propose a novel approach for quantifying deviations from Gaussianity by leveraging the permutation Jensen-Shannon distance. Using stable distributions as a flexible framework, we analyze the effects of skewness and heavy tails in…
Quantum relative entropy, a quantum generalization of the renowned Kullback-Leibler divergence, serves as a fundamental measure of the distinguishability between quantum states and plays a pivotal role in quantum information science.…
We conformally weld (via "quantum zipping") two boundary arcs of a Liouville quantum gravity random surface to generate a random curve called the Schramm-Loewner evolution (SLE). We develop a theory of quantum fractal measures (consistent…
A brief comment on A variational Bayesian approach for inverse problems with skew-t error distributions (Guha et al., Journal of Computational Physics 301 (2015) 377-393) is given in this letter.
The Cauchy-Schwarz (CS) divergence was developed by Pr\'{i}ncipe et al. in 2000. In this paper, we extend the classic CS divergence to quantify the closeness between two conditional distributions and show that the developed conditional CS…
A new class of weighted spectral geometric means has recently been introduced. In this paper, we present its inequalities in terms of the L\"{o}wner order, operator norm, and trace. Moreover, we establish a log-majorization relationship…