相关论文: Checking $2 \times M$ separability via semidefinit…

We provide quantitative bounds on the characterisation of multiparticle separable states by states that have locally symmetric extensions. The bounds are derived from two-particle bounds and relate to recent studies on quantum versions of…

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…

We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure…

We present a quasipolynomial-time algorithm for solving the weak membership problem for the convex set of separable, i.e. non-entangled, bipartite density matrices. The algorithm decides whether a density matrix is separable or whether it…

After introducing the partially separable concept, we proved the equivalence between the partial separability of a given $m$-partite subsystem with $m$ qubits and the purity of states of this $m$-partite subsystem for a pure state in…

The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…

We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…

Let K, K' be convex cones residing in finite-dimensional real vector spaces E, E'. An element in the tensor product E \otimes E' is K \otimes K'-separable if it can be represented as finite sum \sum_l x_l \otimes x'_l with x_l \in K and…

A symmetric matrix $C$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $C=BB^T$. The CP-completion problem is to study whether we can assign values to the missing entries of a partial matrix (i.e.,…

We consider the two categories of termination problems of quantum programs with nondeterminism: 1) Is an input of a program terminating with probability one under all schedulers? If not, how can a scheduler be synthesized to evidence the…

In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…

We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the…

A symmetric tensor, which has a symmetric nonnegative decomposition, is called a completely positive tensor. We consider the completely positive tensor decomposition problem. A semidefinite algorithm is presented for checking whether a…

A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the…

Two matrices are said to be principal minor equivalent if they have equal corresponding principal minors of all orders. We give a characterization of principal minor equivalence and a deterministic polynomial time algorithm to check if two…

We derive and study a significance test for determining if a panel of functional time series is separable. In the context of this paper, separability means that the covariance structure factors into the product of two functions, one…

The problem of matrix completion and decomposition in the cone of positive semidefinite (PSD) matrices is a well-understood problem, with many important applications in areas such as linear algebra, optimization, and control theory. This…

The structure of the set of positivity-preserving maps between matrix algebras is notoriously difficult to describe. The notable exceptions are the results by St{\o}rmer and Woronowicz from 1960s and 1970s settling the low dimensional…

We investigate the problem of finding the optimal convex decomposition of a bipartite quantum state into a separable part and a positive remainder, in which the weight of the separable part is maximal. This weight is naturally identified…

Separability criteria are typically of the necessary, but not sufficient, variety, in that satisfying some separability criterion, such as positivity of eigenvalues under partial transpose, does not strictly imply separability. Certifying…