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We describe a purely algebraic method for finding the best separable approximation to a mixed state of a composite 2x2 quantum system, consisting of a decomposition of the state into a linear combination of a mixed separable part and a pure…

We provide algorithms for efficiently addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with low overhead by the more realistic model of a distributed quantum computer. As a result, the…

We study the concurrence for arbitrary N-partite W-class states based on the (N-1)-partite partitions of subsystems by taking account to the structures of W-class states. By using the method of permutation and combination we give analytical…

Finding the closest separable state to a given target state is a notoriously difficult task, even more difficult than deciding whether a state is entangled or separable. To tackle this task, we parametrize separable states with a neural…

We develop a numerical algorithm to calculate the degrees of irreducible multiparty correlations for an arbitrary multiparty quantum state, which is efficient for any quantum state of up to five qubits. We demonstrate the power of the…

Quantum computers can solve specific complex tasks for which no reasonable-time classical algorithm is known. Quantum computers do however also offer inherent security of data, as measurements destroy quantum states. Using shared entangled…

Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task…

We study the problem of detecting multipartite entanglement among indistinguishable fermionic particles. A multipartite concurrence for pure states of $N$ identical fermions, each one having a $d$-dimensional single-particle Hilbert space,…

We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our…

We compute the probability that a bipartite quantum state is separable by Monte Carlo sampling. This is carried out for rebits, qubits and quaterbits. We sampled $5\times 10^{11}$ points for each of these three cases. The results strongly…

We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility…

To determine whether a given multipartite quantum state is separable with respect to some partition we construct a family of entanglement measures R_m. This is done utilizing generalized concurrences as building blocks which are defined by…

In this paper, we consider the problem of unambiguous discrimination between a set of mixed quantum states. We first divide the density matrix of each mixed state into two parts by the fact that it comes from ensemble of pure quantum…

Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient…

A general and computable criterion for k-(in)separability in continuous multipartite quantum systems is presented. The criterion can be experimentally implemented with a finite and comparatively low number of local observables. We discuss…

This paper proposes distributed algorithms for solving linear equations to seek a least square solution via multi-agent networks. We consider that each agent has only access to a small and imcomplete block of linear equations rather than…

We study the entanglement of a multipartite quantum state. An inequality between the bipartite concurrence and the multipartite concurrence is obtained. More effective lower and upper bounds of the multipartite concurrence are obtained. By…

We study the entanglement of tripartite quantum states and provide analytical lower bound of concurrence in terms of the concurrence of sub-states. The lower bound may improve all the existing lower bounds of concurrence. The approach is…

We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the…

Identifying the $k$-partite entanglement and $k$-nonseparability of general $N$-partite quantum states are fundamental issues in quantum information theory. By use of computable inequalities of nonlinear operators, we present some simple…