Related papers: Characterizing High Schmidt Number Witnesses in Ar…
In quantum information theory, the Schmidt rank is a fundamental measure for the entanglement dimension of a pure bipartite state. Its natural definition uses the Schmidt decomposition of vectors on bipartite Hilbert spaces, which does not…
Entanglement, while being critical in many quantum applications, is difficult to characterize experimentally. While entanglement witnesses based on the fidelity to the target entangled state are efficient detectors of entanglement, they in…
Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two…
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…
We study entanglement in a system of three coupled quantum harmonic oscillators. Specifically, we use the Schmidt decomposition to analyze how the entanglement is distributed among the three subsystems. The Schmidt decomposition is a…
Quantum entanglement is a fascinating phenomenon, especially if it is observed at the macroscopic scale. Importantly, macroscopic quantum correlations can be revealed only by accurate measurement outcomes and strategies. Here, we formulate…
We focus on determining the separability of an unknown bipartite quantum state $\rho$ by invoking a sufficiently large subset of all possible entanglement witnesses given the expected value of each element of a set of mutually orthogonal…
Experimental procedures are presented for the rapid detection of entanglement of unknown arbitrary quantum states. The methods are based on the entanglement criterion using accessible correlations and the principle of correlation…
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 consider multipartite quantum state discrimination and show that the minimum-error discrimination by separable measurements is closely related to the concept of entanglement witness. Based on the properties of entanglement witness, we…
The purpose of this paper is to study entanglement of quantum states by means of Schmidt decomposition. The notion of Schmidt information which characterizes the non-randomness of correlations between two observers that conduct measurements…
We derive a set of algebraic equations, the so-called multipartite separability eigenvalue equations. Based on their solutions, we introduce a universal method for the construction of multipartite entanglement witnesses. We witness…
We study Schmidt rank for a vector (i.e., a pure state) and Schmidt number for a mixed state which are entanglement measures. We show that if a subspace of a certain bipartite system contains no vector of Schmidt rank $\leqslant k$, then…
A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms.…
Entanglement is a central resource in quantum information science, yet its structure in high dimensions remains notoriously difficult to characterize. One of the few general results on high-dimensional entanglement is given by peel-off…
The thesis includes the original results of our articles [30, 37, 40, 42, 51, 53, 75]. A method is developed to compute analytically entanglement measures of three-qubit pure states. Owing to it closed-form expressions are presented for the…
We address the problem of optimising entanglement witnesses when a limited fixed set of local measurements can be performed on a bipartite system, thus providing a procedure, feasible also for experiments, to detect entangled states using…
We introduce an experimental procedure for the detection of quantum entanglement of an unknown quantum state with as few measurements as possible. The method requires neither a priori knowledge of the state nor a shared reference frame…
Creating large-scale entanglement lies at the heart of many quantum information processing protocols and the investigation of fundamental physics. For multipartite quantum systems, it is crucial to identify not only the presence of…
We propose a device-independent null witness dimensionality test with bipartite measurements and input from two separate parties. The dimension is determined from the rank of the matrix of measurements for pairs of states prepared by the…