Related papers: Strong NP-Hardness of the Quantum Separability Pro…
Consider a ring of N qubits in a translationally invariant quantum state. We ask to what extent each pair of nearest neighbors can be entangled. Under certain assumptions about the form of the state, we find a formula for the maximum…
This paper deals with the entanglement, as quantified by the negativity, of pure quantum states chosen at random from the invariant Haar measure. We show that it is a constant (0.72037) multiple of the maximum possible entanglement. In line…
We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We…
We develop separability criteria to identify non-$k$-separability $(k = 2,3,\ldots,n)$ and genuine multipartite entanglement in different classes of mixed $n$-partite quantum states using elements of density matrices. With the help of these…
Entanglement is at the heart of most quantum information tasks, and therefore considerable effort has been made to find methods of deciding the entanglement content of a given bipartite quantum state. Here, we prove a fundamental limitation…
One of the most fascinating aspects of quantum networks is their capability to distribute entanglement as a nonlocal communication resource. In a first step, this requires network-ready devices that can generate and store entangled states.…
We consider entanglement detection for quantum key distribution systems that use two signal states and continuous variable measurements. This problem can be formulated as a separability problem in a qubit-mode system. To verify…
Given a finite number $N$ of copies of a qubit state we compute the maximum fidelity that can be attained using joint-measurement protocols for estimating its purity. We prove that in the asymptotic $N\to\infty$ limit, separable-measurement…
Recent efforts have focused on characterizing the set of separable states that cannot be made entangled by any global unitary transformation. Here we characterize the set of states whose entanglement content cannot be increased under any…
The interleaving distance is arguably the most prominent distance measure in topological data analysis. In this paper, we provide bounds on the computational complexity of determining the interleaving distance in several settings. We show…
We present the variational separability verifier (VSV), which is a novel variational quantum algorithm (VQA) that determines the closest separable state (CSS) of an arbitrary quantum state with respect to the Hilbert-Schmidt distance (HSD).…
We investigate the problem of distinguishing between separable and entangled states of two quantum wave packets, one of which falls into a black hole. Intuitively, one might expect the two scenarios to be indistinguishable, since the…
Quantifying entanglement for multipartite quantum state is a crucial task in many aspects of quantum information theory. Among all the entanglement measures, relative entropy of entanglement $E_{R}$ is an outstanding quantity due to its…
It is known that relative entropy of entanglement for entangled state $\rho$ is defined via its closest separable (or positive partial transpose) state $\sigma$. Recently, it has been shown how to find $\rho$ provided that $\sigma$ is given…
An important open problem in quantum information theory is the question of the existence of NPT bound entanglement. In the past years, little progress has been made, mainly because of the lack of mathematical tools to address the problem.…
The achievement of quantum supremacy boosted the need for a robust medium of quantum information. In this task, higher-dimensional qudits show remarkable noise tolerance and enhanced security for quantum key distribution applications.…
The problem on detecting the entanglement of a bipartite state is significant in quantum information theory. In this article, we apply the Ky Fan norm to the revised realignment matrix of a bipartite state. Specifially, we consider a family…
Every entangled state can be perturbed, for instance by decoherence, and stay entangled. For a large class of pure entangled states, we show how large the perturbation can be. Our class includes all pure bipartite and all maximally…
We consider a class of entangled states of a quantum system (S) and a second system (A) where pure states of the former are correlated with mixed states of the latter, and work out the entanglement measure with reference to the nearest…
We discuss the critical point $x_c$ separating the quantum entangled and separable states in two series of N spins S in the simple mixed state characterized by the matrix operator $\rho=x|\tilde{\phi}><\tilde{\phi}| + \frac{1-x}{D^N}…