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In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
It is known that the security evaluation can be done by smoothing of R\'{e}nyi entropy of order 2 in the classical and quantum settings when we apply universal$_2$ hash functions. Using the smoothing of Renyi entropy of order 2, we derive…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
The similarity of local atomic environments is an important concept in many machine-learning techniques which find applications in computational chemistry and material science. Here, we present and discuss a connection between the…
Maximum entropy (MAXENT) method has a large number of applications in theoretical and applied machine learning, since it provides a convenient non-parametric tool for estimating unknown probabilities. The method is a major contribution of…
Audenaert and Datta recently introduced a two-parameter family of relative R\'{e}nyi entropies, known as the $\alpha$-$z$-relative R\'{e}nyi entropies. The definition of the $\alpha$-$z$-relative R\'{e}nyi entropy unifies all previously…
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…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various…
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.…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
A quantum model can be mapped to a classical model in one higher dimension. Here we introduce a finite-temperature correlation measure based on a reduced density matrix rho_A obtained by cutting the classical system along the imaginary time…
We consider a quantum quasi-relative entropy $S_f^K$ for an operator $K$ and an operator convex function $f$. We show how to obtain the error bounds for the monotonicity and joint convexity inequalities from the recent results for the…
We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources, i.e., sources that emit one of two possible quantum states with given prior probabilities. Such a…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…
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…
We discuss the dependence of the Shannon entropy of normalized finite rank-1 POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be…