相关论文: A tensor version of the quantum Wielandt theorem

We prove a local limit theorem, i.e. a central limit theorem for densities, for a sequence of independent and identically distributed random variables taking values on an abstract Wiener space; the common law of those random variables is…

We proof a uniqueness and periodicity theorem for bounded solutions of uniformly elliptic equations in certain unbounded domains.

We prove, under suitable conditions, a lower bound on the number of pinned distances determined by small subsets of two-dimensional vector spaces over fields. For finite subsets of the Euclidean plane we prove an upper bound for their…

We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…

A brief history of the investigation of the Weil-Petersson curvature and a summary of Teichm\"{u}ller theory are provided. A report is presented on the program to describe an intrinsic geometry with the Weil-Petersson metric and…

One of the main goals in the study of quantum nonlocality is to determine the maximum violation achieved by quantum correlations in a Bell scenario. However, given a Bell inequality, there is no general algorithm to perform this task. As an…

We generalize the notions of asymptotic dimension and coarse embeddings from metric spaces to quantum metric spaces in the sense of Kuperberg and Weaver. We show that quantum asymptotic dimension behaves well with respect to metric…

In this paper, we present a new approach of creating PTAS to the TSP problems by defining a bounded-curvature surface embedded spaces. Using this definition we prove: - A bounded-curvature surface embedded spaces TSP admits to a PTAS. -…

We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity…

Consider a Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem…

We demonstrate that projected entangled-pair states (PEPS) are able to represent ground states of critical, fermionic systems exhibiting both 1d and 0d Fermi surfaces on a 2D lattice with an efficient scaling of the bond dimension.…

While von Neumann entropies for subregions in quantum field theory universally contain ultraviolet divergences, differences between von Neumann entropies are finite and well-defined in many physically relevant scenarios. We demonstrate that…

We construct a wide class of bounded continuous variables observables that lead to violations of Bell inequalities for the EPR state and give an intuitive Wigner function explanation how to predetermine which operators won't ever exceed the…

We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs. Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we restrict ourselves to the normalized Laplacian and, more…

In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.

The infinite projected entangled pair states (iPEPS) technique [J. Jordan {\it et al.}, Phys. Rev. Lett. {\bf 101}, 250602 (2008)] has been widely used in the recent years to assess the properties of two-dimensional quantum systems, working…

A universal geometric inequality for bodies relating energy, size, angular momentum, and charge is naturally implied by Bekenstein's entropy bounds. We establish versions of this inequality for axisymmetric bodies satisfying appropriate…

The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…

The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…

We prove a parametrized compactness theorem on manifolds of bounded Ricci curvature, upper bounded diameter and lower bounded injectivity radius.