Related papers: Constructing entanglement witnesses for infinite-d…
We show how to quantify tri-partite entanglement using entropies derived from experimental correlations. We use a multi-partite generalization of the entanglement of formation that is greater than zero if and only if the state is genuinely…
We consider multipartite quantum state discrimination and provide a specific relation between the properties of entanglement witness and quantum nonlocality inherent in the confidence of measurements. We first provide the definition of the…
Recently, a toolkit of highly symmetric techniques employing matrix inequalities has been developed to detect entanglement in various ways. Here we unifiedly explain in detail these methods, and expand them to a new family of positive maps…
Efficient certification and quantification of high dimensional entanglement of composite systems are challenging both theoretically as well as experimentally. Here, we demonstrate that several entanglement detection methods can be…
We present a construction of new bound entangled states from given bound entangled states for arbitrary dimensional bipartite systems. One way to construct bound entangled states is to show that these states are PPT (positive partial…
We provide a new extension of entanglement witnesses for $\mathbb{C}^{d_{1}}\otimes\mathbb{C}^{d_{2}}$ systems. Our construction preserves the properties of indecomposability and spanning property of entanglement witnesses. We show how our…
Entanglement detection typically relies on linear inequalities for mean values of certain observables (entanglement witnesses), where violation indicates entanglement. We provide a general method to improve any of these inequalities for…
Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin -- a mirrored EW -- whereby two EWs related by mirroring can…
The entanglement content of high-dimensional random pure states is almost maximal, nevertheless, we show that, due to the complexity of such states, the detection of their entanglement using witness operators is rather difficult. We discuss…
Dicke states are a family of multi-qubit quantum states with interesting entanglement properties and have been observed in many experiments. We construct entanglement witnesses for detecting genuine multiparticle entanglement in the…
We apply the generalised concept of witness operators to arbitrary convex sets, and review the criteria for the optimisation of these general witnesses. We then define an embedding of state vectors and operators into a higher-dimensional…
Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme's validity via the probability that…
Recently, there are tremendous developments on the number of controllable qubits in several quantum computing systems. For these implementations, it is crucial to determine the entanglement structure of the prepared multipartite quantum…
The geometric measure of entanglement is an approach to quantifying entanglement that is based on the Hilbert-space distance (or, equivalently, angle) between pure states and their best unentangled approximants. An entanglement witness is…
We present a survey on mathematical topics relating to separable states and entanglement witnesses. The convex cone duality between separable states and entanglement witnesses is discussed and later generalized to other families of…
We introduce two entanglement conditions that take the form of inequalities involving expectation values of operators. These conditions are sufficient conditions for entanglement, that is if they are satisfied the state is entangled, but if…
We study the problem of witnessing entanglement among indistinguishable particles. For this purpose, we derive a set of equations which results in necessary and sufficient conditions for probing multipartite entanglement between arbitrary…
A typical concept in quantum state analysis is based on the idea that states in the vicinity of some pure entangled state share the same properties; implying that states with a high fidelity must be entangled. States whose entanglement can…
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…
A generic algorithm is developed to reduce the problem of obtaining linear and nonlinear entanglement witnesses of a given quantum system, to convex optimization problem. This approach is completely general and can be applied for the…