Related papers: Building separable approximations for quantum stat…
Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or…
Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and…
Although tensor network states constitute a broad range of exotic quantum states, their realization is challenging and often requires resources whose depth scales with system size. In this work, we explore criteria on the local tensors for…
We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the…
According to usual definitions, entangled states cannot be given a separable decomposition in terms of products of local density operators. If we relax the requirement that the local density operators be positive, then an entangled quantum…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
In recent years considerable progress has been made towards developing a general theory of quantum entanglement. In particular, criteria to decide whether a given quantum state is entangled are of high theoretical and practical interest.…
Quantifying entanglement in quantum systems is an important yet challenging task due to its NP-hard nature. In this work, we propose an efficient algorithm for evaluating distance-based entanglement measures. Our approach builds on…
Optimizing over separable quantum objects is challenging for two key reasons: determining separability is NP-hard, and the dimensionality of the problem grows exponentially with the number of qubits. We address both challenges by…
Suppose we have an unknown multipartite quantum state, how can we experimentally find out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already…
A geometric understanding of entanglement is proposed based on local measurements. Taking recourse to the general structure of density matrices in the framework of Euclidean geometry, we first illustrate our approach for bipartite Werner…
We introduce a new technique to detect separable states using semidefinite programs. This approach provides a sufficient condition for separability of a state that is based on the existence of a certain local linear map applied to a known…
We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values of Hermitian operators…
The task of classifying the entanglement properties of a multipartite quantum state poses a remarkable challenge due to the exponentially increasing number of ways in which quantum systems can share quantum correlations. Tackling such…
Multipartite entanglement is a valuable resource for quantum technologies. However, detecting this resource can be challenging: for genuine multipartite entanglement, the detection may require global measurements that are hard to implement…
The description of the complex separability structure of quantum states in terms of partially ordered sets has been recently put forward. In this work, we address the question of how to efficiently determine these structures for unknown…
We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient $k$-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems.…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…
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…