Related papers: Inseparability criterion for continuous variable s…
We study separability criteria in multipartite quantum systems of arbitrary dimensions by using the Bloch representation of density matrices. We first derive the norms of the correlation tensors and obtain the necessary conditions for…
We give a new separability criterion, a necessary condition for separability of $N$-partite quantum states. The criterion is based on the Bloch representation of a $N$-partite quantum state and makes use of multilinear algebra, in…
We investigate the separability properties of quantum two-party Gaussian states in the framework of the operator formalism for the density operator. Such states arise as natural generalizations of the entangled state originally introduced…
By using the algebraic separability criterion of R. Simon, we present an explicit determination of squeezing parameters for which the P-representation condition saturates the $Sp(2,R)\otimes Sp(2,R)$ invariant separability condition for…
We compare theoretically the tripartite entanglement available from the use of three concurrent $\chi^{(2)}$ nonlinearities and three independent squeezed states mixed on beamsplitters, using the van Loock-Furusawa inequalities. We also…
We explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial…
We show that for a fixed amount of entanglement, two-mode squeezed states are those that maximize Einstein-Podolsky-Rosen-like correlations. We use this fact to determine the entanglement of formation for all symmetric Gaussian states…
For any unitarily invariant convex function F on the states of a composite quantum system which isolates the trace there is a critical constant C such that F(w)<= C for a state w implies that w is not entangled; and for any possible D > C…
We introduce examples of three- and four-mode entangled Gaussian mixed states that are not detected by the scaling and Peres-Horodecki separability criteria. The presented modification of the scaling criterion resolves this problem. Also it…
We classify the entanglement of two--mode Gaussian states according to their degree of total and partial mixedness. We derive exact bounds that determine maximally and minimally entangled states for fixed global and marginal purities. This…
We propose a range criterion which is a sufficient and necessary condition satisfied by two pure states transformable with each other under reversible stochastic local operations assisted with classical communication. We also provide a…
Recently, a new and powerful separability criterion was introduced in [O. Rudolph, quant-ph/0202121] and [Chen {\it et al.}, quant-ph/0205017]. Composing the main idea behind the above criterion and the necessary and sufficient condition in…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
Multipartite entanglement detection is crucial for the develop of quantum information science and quantum computation, communication, simulation and metrology tasks. In contrast to experiments, where several handreds of qubits have been…
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex…
We establish a mapping between a continuous variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a…
We introduce the notion of "separation of conditions" meaning that a description of statistical data obtained from experiments, performed under a set of different conditions, allows for a decomposition such that each partial description…
We study the detection of continuous-variable entanglement, for which most of the existing methods designed so far require a full specification of the devices, and we present protocols for entanglement detection in a scenario where the…
Starting with a set of conditions for bipartite separability of arbitrary quantum states in any dimension and expressed in terms of arbitrary operators whose commutator is a $c$-number, we derive a hierarchy of conditions for tripartite…
The known Peres-Horodecki criterion and scaling criterion of separability are considered on examples of three-mode and four-mode Gaussian states of electromagnetic field. It is shown that the principal minors of the photon quadrature…