相关论文: Covariance matrices and the separability problem

High-dimensional entanglement has been identified as an important resource in quantum information processing, and also as a main obstacle for simulating quantum systems. Its certification is often difficult, and most widely used methods for…

Continuous variables systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as…

We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…

Separability and entanglement for n-qubits systems are quantified by using Hilbert-Schmidt (HS) decompositions in which the density matrices are decomposed into various terms representing certain one qubit, two-qubits,and larger qubits…

If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present…

Understanding the distribution of quantum entanglement over many parties is a fundamental challenge of quantum physics and is of practical relevance for several applications in the field of quantum information. Here we use methods from…

We analyze and compare the mathematical formulations of the criterion for separability for bipartite density matrices and the Bell inequalities. We show that a violation of a Bell inequality can formally be expressed as a witness for…

Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…

We use the generalized concurrence approach to investigate the general multipartite separability problem. By extending the preconcurrence matrix formalism to arbitrary multipartite systems, we show that the separability problem can be…

We review the problem of discriminating entangled states from separable states for bipartite systems. We formally define what entangled states are, present some important criteria to detect entanglement, and show how they can be classified…

We explain several separability criteria which rely on uncertainty relations. For the derivation of these criteria uncertainty relations in terms of variances or entropies can be used. We investigate the strength of the separability…

We show that higher order inter-group covariances involving even number of qubits are necessarily positive semidefinite for N qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads…

We explore the possibility of entanglement detection in continuous variable systems by entanglement witnesses based on covariance matrices, constructible from random homodyne measurements. We propose new linear constraints characterizing…

This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the…

We propose an entanglement measure for two qudits based on the covariances of a set of generators of the su(N) algebra. In particular, we represent this measure in terms of the mutually unbiased projectors for N prime. For pure states this…

Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of…

We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called 'separability' measure, reveals which of the subsystems are…

We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally…

The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions…

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…