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We present a diffeomorphism-invariant formulation of differential entropy for Riemannian spaces, providing a fine-grained, coordinate-independent notion of quantum information for continuous variables in physical space. To this end, we…
We show that a von Neumann measurement on a part of a composite quantum system unavoidably creates distillable entanglement between the measurement apparatus and the system if the state has nonzero quantum discord. The minimal distillable…
We study the fundamental properties of the quantum f-relative entropy, where f(.) is an operator convex function. We give the equality conditions under monotonicity and joint convexity, and these conditions are more general than, since they…
We formulate a novel approach to decoherence based on neglecting observationally inaccessible correlators. We apply our formalism to a renormalised interacting quantum field theoretical model. Using out-of-equilibrium field theory…
There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty…
Currently, 'time' does not play any essential role in quantum information theory. In this sense, quantum information theory is underdeveloped similarly to how quantum physics was underdeveloped before Erwin Schrodinger introduced his famous…
In quantum information geometry, the curvature of von-Neumann entropy and relative entropy induce a natural metric on the space of mixed quantum states. Here we use this information metric to construct a random matrix ensemble for states…
In this work we investigate the conditions for quantum back action to result in a phase transition in the information dynamics of a monitored system. We introduce a framework that captures a wide range of experiments encompassing probes…
We define a large class of quantum sources and prove a quantum analog of the asymptotic equipartition property. Our proof relies on using local measurements on the quantum source to obtain an associated classical source. The classical…
Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state…
This article addresses the issue of the proof of the entropy power inequality (EPI), an important tool in the analysis of Gaussian channels of information transmission, proposed by Shannon. We analyse continuity properties of the mutual…
The chain rule for the Shannon and von Neumann entropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here we consider the chain rule for the more general smooth…
How much information about an unknown quantum state can be obtained by a measurement? We propose a model independent answer: the information obtained is equal to the minimum entropy of the outputs of the measurement, where the minimum is…
We consider two fundamental tasks in quantum information theory, data compression with quantum side information as well as randomness extraction against quantum side information. We characterize these tasks for general sources using…
Given an independent and identically distributed source $X = \{X_i \}_{i=1}^{\infty}$ with finite Shannon entropy or differential entropy (as the case may be) $H(X)$, the non-asymptotic equipartition property (NEP) with respect to $H(X)$ is…
We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum…
In this work we investigate the asymptotic behavior related to the quantum privacy for multipartite systems. In this context, an inequality for quantum privacy was obtained by exploiting of quantum entropy properties. Subsequently, we…
Bayesian integral functional measure of entropy-uncertainty (EF) on trajectories of Markov multi-dimensional diffusion process is cutting off by interactive impulses (controls). Each cutoff minimax of EF superimposes and entangles…
Entropy is one of the central quantities in thermodynamics, whose flow between two systems determines the statistics of energy transfers. In quantum systems entropy is non-linear in density matrix whose time evolution is cumbersome. Using…
Comparing with traditional learning criteria, such as mean square error (MSE), the minimum error entropy (MEE) criterion is superior in nonlinear and non-Gaussian signal processing and machine learning. The argument of the logarithm in…