Related papers: Entangleability of cones
Starting from an arbitrary endomorphism \alpha of a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,\alpha) but also on the choice of an ideal…
It is known that probabilistically mixing an arbitrary pair of pure quantum states, one of which is entangled and the other product, in any bipartite quantum system, one always obtains an entangled state, provided the entangled state of the…
We present a novel approach to look for the existence of maximum entanglement in a system of two identical quantum dots coupled by the Forster process and interacting with a classical laser field. Our approach is not only able to explain…
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We…
We consider four norms on tensor product spaces that have appeared in quantum information theory and demonstrate duality relationships between them. We show that the product numerical radius is dual to the robustness of entanglement, and we…
We establish uniqueness and regularity results for tangent cones (at a point or at infinity) with isolated singularities arising from a given immersed stable minimal hypersurface with suitably small (non-immersed) singular set. In…
In the finite-dimensional case, we present a new approach to the theory of cones with a mapping cone symmetry, first introduced by St{\o}rmer. Our method is based on a definition of an inner product in the space of linear maps between two…
We evaluate the entanglement entropy of a non-minimal coupling Einstein-scalar theory with two approaches in classical Euclidean gravity. By analysing the equation of motion, we find that the entangled surface is restricted to be a minimal…
Quite recently, Cai et al. [arXiv:2006.07165v1] proposed a new concept "absolutely entangled set" for bipartite quantum systems: for any possible choice of global basis, at least one state of the set is entangled. There they presented a…
In this paper, we prove that the product of a paired calibrated set and a set of codimension 1 calibrated by a coflat calibration with small singularity set is Almgren minimal. This is motivated by the attempt to classify all possible…
In continuous quantum field theories, the entanglement entropy of a subsystem with sharp corners on its boundary exhibits a universal corner-dependent contribution. We study this contribution through the lens of lattice discretization, and…
The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor product of two bipartite entangled states by merging two systems. We show that the…
Sets of $d\times d$ matrices sharing a common invariant cone enjoy special properties, which are widely used in applications. However, finding this cone or even proving its existence/non-existence is hard. This problem is known to be…
Tensor networks are generated by a set of small rank tensors and define many-body quantum states in a succinct form. The corresponding map is not one-to-one: different sets of tensors may generate the very same state. A fundamental question…
This article provides a convenient framework for quantitative evaluation of the entanglement generated when two structureless, distinguishable particles scatter non-relativistically in one dimension. It explores how three factors determine…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
This paper completes a fundamental construction in Alexandrov geometry. Previously we gave a new construction of metric spaces with curvature bounds either above or below, namely warped products with intrinsic metric space base and fiber,…
For a discrete group $G$, we develop a `$G$-balanced tensor product' of two coactions $(A,\delta)$ and $(B,\epsilon)$, which takes place on a certain subalgebra of the maximal tensor product $A\otimes_{\max} B$. Our motivation for this is…
We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly…
The tensor train decomposition decomposes a tensor into a "train" of 3-way tensors that are interconnected through the summation of auxiliary indices. The decomposition is stable, has a well-defined notion of rank and enables the user to…