Related papers: Infinite Dimensional Asymmetric Quantum Channel Di…
It is shown that a receiver equipped with two antennas may null an arbitrary large number of spatial directions to any desired accuracy, while maintaining the interference-free signal-to-noise ratio, by judiciously adjusting the distance…
A nonlinear adaptive procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we…
For the sandwiched R\'enyi entropy the conditional entropy can be defined two ways: $\widetilde{H}^\downarrow_\alpha(A|B)_\rho, \widetilde{H}^\uparrow_\alpha(A|B)_\rho$. In the limiting case, $\alpha=1$, both definitions consolidate into…
R\'enyi divergence is related to R\'enyi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as a measure of information that satisfies almost the same…
Surprisingly often decoherence is due to classical fluctuations of ambient fields and may thus be described in terms of random unitary (RU) dynamics. However, there are decoherence channels where such a representation cannot exist. Based on…
Fawzi and Fawzi recently defined the sharp R\'enyi divergence, $D_\alpha^\#$, for $\alpha \in (1, \infty)$, as an additional quantum R\'enyi divergence with nice mathematical properties and applications in quantum channel discrimination and…
This paper presents a systematic study of adversarial hypothesis testing for both quantum-quantum (QQ) and classical-quantum (CQ) channels. Unlike conventional channel discrimination, we consider a framework where the sender, Alice, selects…
Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation matrices. Quantum mechanically these matrices are doubly stochastic channels, i.e. they are completely positive maps preserving both the trace…
Recently, a new notion of quantum R\'enyi divergences has been introduced by M\"uller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J.Math.Phys. 54:122203, (2013), and Wilde, Winter, Yang, Commun.Math.Phys. 331:593--622, (2014), that has…
We introduce the two-way Gaussian interference channel in which there are four nodes with four independent messages: two-messages to be transmitted over a Gaussian interference channel in the $\rightarrow$ direction, simultaneously with…
Quantum channel, as the information transmitter, is an indispensable tool in quantum information theory. In this paper, we study a class of special quantum channels named the mixed-permutation channels. The properties of these channels are…
The parallel dynamics of extremely diluted symmetric Q-Ising neural networks is studied for arbitrary Q using a probabilistic approach. In spite of the extremely diluted architecture the feedback correlations arising from the symmetry…
We derive a novel chain rule for a family of channel conditional entropies, covering von Neumann and sandwiched R\'{e}nyi entropies. In the process, we show that these channel conditional entropies are equal to their regularized version,…
Characterizing those quantum channels that correspond to Markovian time evolutions is an open problem in quantum information theory, even different notions of quantum Markovianity exist. One such notion is that of infinitesimal Markovian…
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
Wide neural networks have proven to be a rich class of architectures for both theory and practice. Motivated by the observation that finite width convolutional networks appear to outperform infinite width networks, we study scaling laws for…
We study natural examples of binary channels with synchronization errors. These include the duplication channel, which independently outputs a given bit once or twice, and geometric channels that repeat a given bit according to a geometric…
We study distributed similarity estimation of quantum channels (DSEC), a primitive for cross-platform verification where two remote quantum devices are compared by estimating the inner product of their Choi states. We show that the optimal…
The dimensionality of entanglement, quantified by the Schmidt number, is a valuable resource for a wide range of quantum information processing tasks. In this work, we introduce the notion of the absolute Schmidt number, referring to states…
At a quantum critical point, bipartite entanglement entropies have universal quantities which are subleading to the ubiquitous area law. For Renyi entropies, these terms are known to be similar to the von Neumann entropy, while being much…