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Quantum technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability of…
We establish a new global endpoint Sobolev inequality for measures that extends the classical theorem of Meyers-Ziemer by placing a maximal function on the right-hand side. This result has several significant consequences. It extends…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincar\'{e} inequalities, general Beckner inequalities...). We also discuss the…
Quantum-correlated networks distribute quantum resources such as squeezed and entangled states. These states are central to modern quantum technology, including photonic quantum computing, quantum communications, non-destructive biological…
Quantum correlations are the singular, defining resource of quantum information science and metrology, forming the basis of every operational advantage that quantum systems hold over classical ones. Yet exact bounds on these…
Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique…
On a stratified Lie group $G$ equipped with hypoelliptic heat kernel measure, we study the behavior of the dilation semigroup on $L^p$ spaces of log-subharmonic functions. We consider a notion of strong hypercontractivity and a strong…
In this paper, we investigate an inverse random source problem concerned with recovering the strength of a random, uncorrelated acoustic source from correlation measurements of emitted time-harmonic acoustic waves. Such problems arise in…
Reversible work extraction from identical quantum systems via collective operations was shown to be possible even without producing entanglement among the sub-parts. Here, we show that implementing such global operations necessarily imply…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
We explore an interplay between an analysis of diffusion flows such as Ornstein--Uhlenbeck flow and Fokker--Planck flow and inequalities from convex geometry regarding the volume product. More precisely, we introduce new types of…
Turbo coding is a powerful class of forward error correcting codes, which can achieve performances close to the Shannon limit. The turbo principle can be applied to the problem of side-information source coding, and we investigate here its…
Partially smoothed information measures are fundamental tools in one-shot quantum information theory. In this work, we determine the exact strong converse exponents of these measures for both pure quantum states and classical states.…
This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows…
We investigate the analytic structure of thermal energy-momentum tensor correlators at large but finite coupling in quantum field theories with gravity duals. We compute corrections to the quasinormal spectra of black branes due to the…
We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing this we extend a characterization of the minimizing…
This paper concerns with the time-reversal characteristics of intrinsic normal diffusion in quantum systems. Time-reversible properties are quantified by the time-reversal test; the system evolved in the forward direction for a certain…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
In the first part of this article we present a growth condition on the potential $q$ in the Schr\"odinger operator $H=-\Delta + q(x)$ in $\mathrm{L}^{2}\left( \mathbb{R}^{n} \right)$ that implies Rosen inequalities for the ground state…