相关论文: Entanglement bases and general structures of ortho…

Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are…

We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…

Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively…

A measure of entanglement production by quantum operations is suggested. This measure is general, being valid for operations over pure states as well as over mixed states, for equilibrium as well as for nonequilibrium processes. The measure…

A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.

We introduce the definition of generic bound entanglement for the case of continuous variables. We provide some examples of bound entangled states for that case, and discuss their physical sense in the context of quantum optics. We rise the…

We present Schmidt decomposition formulas for mutually orthogonal two-qubit pure states and classify orthonormal sets based on their entanglement structure. First, we derive explicit Schmidt decomposition formulas for any pure state and…

We review `particle partitioning entanglement' for itinerant many-particle systems. This is defined as the entanglement between two subsets of particles making up the system. We identify generic features and mechanisms of particle…

An unextendible product basis (UPB) for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state. We give examples of UPBs, and show that the uniform mixed state over the…

From the physical point of view entanglement witnesses define a universal tool for analysis and classification of quantum entangled states. From the mathematical point of view they provide highly nontrivial generalization of positive…

We give an introduction to the theory of multi-partite entanglement. We begin by describing the "coordinate system" of the field: Are we dealing with pure or mixed states, with single or multiple copies, what notion of "locality" is being…

Finite tight frames are interesting in various topics including questions of quantum information. Each complex tight frame leads to a resolution of the identity in the Hilbert space. Symmetric informationally complete measurements are a…

In this paper we study the cohomology of tensor products of symmetric powers of the cotangent bundle of complete intersection varieties in projective space. We provide an explicit description of some of those cohomology groups in terms of…

We study the mathematical structure of superoperators describing quantum measurements, including the \emph{entangling measurement}--the generalization of the standard quantum measurement that results in entanglement between the measurable…

It is shown that quantum devices based only on oscillators cannot serve as the universal quantum computer, despite of entanglement in such devices, which we roughly estimate for the ideal case and for the harmful entanglement with photonic…

We present a framework to study the entanglement structure of a quantum field theory inspired by the formalism of particle detectors in relativistic quantum information. This framework can in principle be used to faithfully capture…

We show that the separability of states in quantum mechanics has a close counterpart in classical physics, and that conditional mutual information (a.k.a. conditional information transmission) is a very useful quantity in the study of both…

We put forward a simple construction of genuinely entangled subspaces -- subspaces supporting only genuinely multipartite entangled states -- of any permissible dimensionality for any number of parties and local dimensions. The method uses…

We present basics of mixed-state entanglement theory. The first part of the article is devoted to mathematical characterizations of entangled states. In second part we discuss the question of using mixed-state entanglement for quantum…

Bound entanglement is a special form of quantum entanglement that cannot be used for distillation, i.e., the local transformation of copies of arbitrarily entangled states into a smaller number of approximately maximally entangled states.…