相关论文: Separability and Entanglement-Breaking in Infinite…

Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement.…

We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…

We prove that an infinitesimally Hilbertian CD(0,N) space containing a line splits as the product of $R$ and an infinitesimally Hilbertian CD(0,N-1) space. By `infinitesimally Hilbertian' we mean that the Sobolev space $W^{1,2}(X,d,m)$,…

We present a general description of separable states in Quantum Mechanics. In particular, our result gives an easy proof that inseparabitity (or entanglement) is a pure quantum (noncommutative) notion. This implies that distinction between…

We consider a quantum system with a finite number of distinguishable quantum states, which may be partitioned freely by a number of quantum particles, assumed to be maximally entangled. We show that if we partition the system into a number…

Shared entanglement can significantly amplify classical correlations between systems interacting over a limited quantum channel. A natural avenue is to use entanglement of the same dimension as the channel because this allows for unitary…

Quantum channels breaking entanglement, incompatibility, or nonlocality are defined as such because they are not useful for entanglement-based, one-sided device-independent, or device-independent quantum information processing,…

We introduce an entanglement criterion to exclude full separability of quantum states. We present numerical evidence that the criterion is necessary and sufficient for the class of GHZ diagonal three-qubit states and estimate the volume of…

We analyze certain class of linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable…

We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We consider a complement of Gabriel's theorem for these representations. Let $\Gamma$ be a finite, connected quiver.…

I consider deterministic distinguishability of a set of orthogonal, bipartite states when only a single copy is available and the parties are restricted to local operations and classical communication, but with the additional requirement…

Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…

This paper studies the class of stochastic maps, or channels, whose action (when tensored with the identity) on an entangled state always yields a separable state. Such maps have a canonical form introduced by Holevo. Such maps are called…

Like a silver thread, quantum entanglement [1] runs through the foundations and breakthrough applications of quantum information theory. It cannot arise from local operations and classical communication (LOCC) and therefore represents a…

A parametrization of multipartite separable states in a finite-dimensional Hilbert space is suggested. It is proved to be a diffeomorphism between the set of zero-trace operators and the interior of the set of separable density operators.…

Localizability of entanglement in fully inseparable states is a key ingredient of assisted quantum information protocols as well as measurement-based models of quantum computing. We investigate the existence of fully inseparable states with…

In this paper, the realignment criterion and the RCCN criterion of separability for states in infinite-dimensional bipartite quantum systems are established. Let $H_A$ and $H_B$ be complex Hilbert spaces with $\dim H_A\otimes H_B=+\infty$.…

Many important sets of normalized states in a multipartite quantum system of finite dimension d, such as the set S of all separable states, are real semialgebraic sets. We compute dimensions of many such sets in several low-dimensional…

In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space…

Entangled systems in experiments may be lost or offline in distributed quantum information processing. This inspires a general problem to characterize quantum operations which result in breaking of entanglement or not. Our goal in this work…