Related papers: A lower bound for the Wehrl entropy of quantum spi…
We present a new lower bound on the differential entropy rate of stationary processes whose sequences of probability density functions fulfill certain regularity conditions. This bound is obtained by showing that the gap between the…
Entanglement in the ground state of the XY model on the infinite chain can be measured by the von Neumann entropy of a block of neighboring spins. We study a double scaling limit: the size of the block is much larger then 1 but much smaller…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
Although there are several proposals of relativistic spin in the literature, the recognition of intrinsicality as a key characteristic for the definition of this concept is responsible for selecting a single tensor operator that adequately…
We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…
Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator…
Entropy and free energy are central concepts in both statistical physics and information theory, with quantum and classical facets. In mathematics these concepts appear quite often in different contexts (dynamical systems, probability…
Relations between Shannon entropy and Renyi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Renyi entropies of order two and three are known, we provide an lower and an upper bound…
Recent time-resolved differential transmission and Faraday rotation measurements of long-lived electron spin coherence in quantum wells displayed intriguing parametric dependencies. For their understanding we formulate a microscopic theory…
It is substantiated that spin is a notion associated with the group of internal symmetry that is tightly connected with the geometrical structure of spacetime. The wave equation for the description of the particles with spin one half is…
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…
We present a controlled method for computing the exchange coupling in strongly correlated one-dimensional electron systems. It is based on the asymptotically exact relation between the exchange constant and the pair-correlation function of…
Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms…
For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove a fractal upper bound on the number of resonances near the essential spectrum, with power determined by the dimension of the trapped set. This covers the case of…
We show the boundedness of entanglement entropy for (bipartite) pure states of quantum spin chains implies split property of subsystems. As a corollary the infinite volume ground states for 1-dim spin chains with the spectral gap between…
Variation of the von Neumann entropy by the Lorentz transformation is discussed. Taking the spin-singlet state in the center of mass frame, the von Neumann entropy in the laboratory frame is calculated from the reduced density matrix…
The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs,…
In this paper it was proved that the quantum relative entropy $D(\sigma \| \rho)$ can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of POVMs. The sequence of POVMs depends on $\rho$,…
We derive upper bounds for spin velocity in half-integer-spin Heisenberg antiferromagnetic chains. We relate these upper bounds to the instability of the gapless state, which is observed in frustrated systems.
In this work, we propose a soft covering problem for fully quantum channels using relative entropy as a criterion for operator closeness. We establish covering lemmas by deriving one-shot bounds on the achievable rates in terms of smooth…