Related papers: Almost sure convergence in quantum spin glasses
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
In this work we consider a problem related to the equilibrium statistical mechanics of spin glasses, namely the study of the Gibbs measure of the random energy model. For solving this problem, new results of independent interest on sums of…
We consider the edge-triangle model (or Strauss model), and focus on the asymptotic behavior of the triangle density when the size of the graph increases to infinity. This random graph belongs to the class of exponential random graphs,…
For a mixed quantum state with density matrix $\rho$ there are infinitely many ensembles of pure quantum states, which average to $\rho$. Starting from Laplace principle of insufficient reason (not to give \emph{a priori} preference to any…
We define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the geometric measure is obtained. It is interesting that this…
We study the large $N$-dimensional limit of the Hessian spectrum at the global minimum of some subclasses of the spherical mixed $p$-spin models. Specifically, we show that its empirical spectral measure converges in probability to a…
We present an approach to approximating static properties of glasses without experimental inputs rooted in the first-principles random structure sampling. In our approach, the glassy system is represented by a collection (composite) of…
Studying the typical entanglement entropy of a bipartite system when averaging over different ensembles of pure quantum states has been instrumental in different areas of physics, ranging from many-body quantum chaos to black hole…
We study the set of random matrix product states (RMPS) introduced in arXiv:0908.3877 as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical…
We study the entanglement properties of random pure stabilizer states in spin-1/2 particles. For two contiguous groups of spins of arbitrary size we obtain a compact and exact expression for the probability distribution for the entanglement…
Quantum experiments usually assume the existence of perfect, classical, reference frames, which allow for the specification of measurement settings (e.g. orientation of the Stern Gerlach magnet in spin measurements) with arbitrary…
We present a universal technique for quantum state estimation based on the maximum-likelihood method. This approach provides a positive definite estimate for the density matrix from a sequence of measurements performed on identically…
We investigate the generic aspects of quantum coherence guided by the concentration of measure phenomenon. We find the average relative entropy of coherence of pure quantum states sampled randomly from the uniform Haar measure and show that…
We propose a scheme for engineering compressed spatial states in a two-dimensional parabolic potential with a spin-orbit coupling by selective spin measurements. This sequence of measurements results in a coordinate-dependent density matrix…
Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals…
We study the experimental signatures of several states of a Bose-Einstein condensate of spin-1 atoms by quantum trajectory simulations of Stern-Gerlach experiments. The measurement process itself creates an apparent random alignment for the…
The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant…
We establish contact between the delocalization properties of pure quantum states, as quantified by their number of principal components, and the average generalized entanglement properties, as quantified by purity measures relative to…
We investigate $\beta$-Generalized random Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We investigate general method names as equilibrium…
In this paper we introduce a nonextensive quantum information theoretic measure which may be defined between any arbitrary number of density matrices, and we analyze its fundamental properties in the spectral graph-theoretic framework.…