Related papers: Semicontinuity bounds for the von Neumann entropy …
The order parameter of a critical system defined in a layered parallel plate geometry subject to Neumann boundary conditions at the limiting surfaces is studied. We utilize a one-particle irreducible vertex parts framework in order to study…
We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation…
We introduce the von Neumann entropy regularization of Unbalanced Non-commutative Optimal Transport, specifically Non-commutative Optimal Transport between semi-definite positive matrices (not necessarily with trace one). We prove the…
Compact algebraic equations are derived, which connect the binding energy and the asymptotic normalization constant (ANC) of a subthreshold bound state with the effective-range expansion of the corresponding partial wave. These relations…
We introduce R\'enyi entropy of a subsystem energy as a natural quantity which closely mimics the behavior of the entanglement entropy and can be defined for all the quantum many body systems. For this purpose, consider a quantum chain in…
Entangled quantum states share properties that do not have classical analogs, in particular, they show correlations that can violate Bell inequalities. It is therefore an interesting question to see what happens to entanglement measures --…
We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S_A=-Tr rho_A log rho_A corresponding to the reduced density matrix rho_A of a subsystem A. For the…
In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…
We establish stability inequalities for the problem of determining the potential, appearing in a Sch\"odinger equation, from partial boundary data in the high frequency limit. These stability inequalities hold under the assumption that the…
We develop a rigorous framework for quantifying quantum coherence in finite-dimensional systems by applying the Schur-Horn majorization theorem to relate eigenvalue distributions and diagonal entries of density matrices. Building on this…
Quantum systems with short range interactions are known to respect an area law for the entanglement entropy: the von Neumann entropy $S$ associated to a bipartition scales with the boundary $p$ between the two parts. Here we study the case…
Maximal repetition of a string is the maximal length of a repeated substring. This paper investigates maximal repetition of strings drawn from stochastic processes. Strengthening previous results, two new bounds for the almost sure growth…
We consider a scalar conservation law with source in a bounded open interval $\Omega\subseteq\mathbb R$. The equation arises from the macroscopic evolution of an interacting particle system. The source term models an external effort driving…
The entanglement entropy (von Neumann entropy) has been used to characterize the complexity of many-body ground states in strongly correlated systems. In this paper, we try to establish a connection between the lower bound of the von…
We study the existence and concentration behavior of the bound states for the following logarithmic Schr\"odinger equation \begin{equation*} \begin{cases} -\varepsilon^2\Delta v+V(x)v=v\log v^2 \ \ &\text {in}\ \ \mathbb R^N,\\ v(x)\to 0 \…
The aim of the work is to give the explicit proofs of the Renyi-entropy uncertainty relations presented in the previous work [A. Rastegin, arXiv:0805.1777]. The relations with both the state-dependent and state-independent entropic bounds…
Semiclassical theory of proximity effect predicts a gap E_g \sim hD/L^2 in the excitation spectrum of a long diffusive SNS junction. Mesoscopic fluctuations lead to anomalously localized states in the normal part of the junction. As a…
We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…
Level density $\rho(E,A)$ is derived for a one-component nucleon system with a given energy $E$ and particle number $A$ within the mean-field semiclassical periodic-orbit theory beyond the saddle-point method of the Fermi gas model. We…
We consider $N\times N$ Hermitian random matrices with independent identical distributed entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. Under suitable assumptions on the…