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The correlation matrix (CM) criterion is a recently derived powerful sufficient condition for the presence of entanglement in bipartite quantum states of arbitrary dimensions. It has been shown that it can be stronger than the positive…
We provide a class of optimal nondecomposable entanglement witnesses for 4N x 4N composite quantum systems or, equivalently, a new construction of nondecomposable positive maps in the algebra of 4N x 4N complex matrices. This construction…
An entanglement witness is an observable with the property that a negative expectation value signals the presence of entanglement. The question arises how a witness can be improved if the expectation value of a second observable is known,…
We construct a family of map which is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still…
Suppose an experimentalist wishes to verify that his apparatus produces entangled quantum states. A finite amount of data cannot conclusively demonstrate entanglement, so drawing conclusions from real-world data requires statistical…
Entanglement witnesses (EWs) are a versatile tool to detect entangled states and characterize related properties of entanglement in quantum information theory. A witness $W$ corresponds to an observable satisfying…
The problem of determining whether a given quantum state is separable is known to be computationally difficult. We develop an approach to this problem based on approximations of convex polytopes in high dimensions. By showing that a convex…
Entanglement certification is crucial in physical experiments, particularly when only partial knowledge of the quantum state is available. In this context, we present an entanglement criterion based on positive but not completely positive…
In this paper we provide an operational method to detect multipartite entanglement in ensemble-based quantum computing. This method is based on the concept of entanglement witness. We decompose the entanglement witness for each class of…
Quantum entanglement lies at the heart of quantum mechanical and quantum information processing. Following the question who \emph{witnesses} entanglement witnesses, we show entangled states play as the role of super entanglement witnesses.…
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 introduce entanglement witnesses for spin ensembles which detect genuine multipartite entanglement using only measurements of the total angular momentum. States that are missed by most other angular-momentum-based witnesses for spin…
We provide a new class of entanglement witnesses for $d \ot d$ systems (two qudits). Our construction generalizes the one proposed recently by Jafarizadeh et al. for $d=3$ and $d=4$ on the basis of semidefinite linear programming. Moreover,…
Entanglement, a critical resource for quantum information processing, needs to be witnessed in many practical scenarios. Theoretically, witnessing entanglement is by measuring a special Hermitian observable, called entanglement witness…
Entanglement is a key resource for quantum information processing. A widely used tool for detecting entanglement is entanglement witness, where the measurement of the witness operator is guaranteed to be positive for all separable states…
Verification of entanglement is an important tool to characterize sources and devices for use in quantum computing and communication applications. In a vast majority of experiments entanglement witnesses (EW) are used in order to prove the…
We investigate the detection of entanglement in $n$-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and non-separable mixed quantum states. No numerical optimization or eigenvalue evaluation…
A convergent iterative procedure is proposed for the calculation of the relative entropy of entanglement of a given bipartite quantum state. When this state turns out to be non-separable the algorithm provides the corresponding optimal…
Two kinds of Bell-states diagonal (BSD) entanglement witnesses (EW) are constructed by using the algebra of Dirac $\gamma$ matrices in the space-time of arbitrary dimension $d$, where the first kind can detect some BSD relativistic and…
A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. Every symmetric operator, represented by a symmetric matrix with only two nonzero elements, and their…