Related papers: Entanglement measures and the Hilbert-Schmidt dist…
Measurement interaction between a measured object and a measuring instrument, if both are initially in a pure state, produces a (final) bipartite entangled state vector. The quasi-classical part of the correlations in it is connected with…
Several inequivalent definitions of the geometric measure of entanglement (GM) have been introduced and studied in the past. Here we review several known and new definitions, with the qualifying criterion being that for pure states the…
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…
The geometric measure of entanglement (GME) quantifies how close a multi-partite quantum state is to the set of separable states under the Hilbert-Schmidt inner product. The GME can be non-multiplicative, meaning that the closest product…
In this paper, we investigate a genuine multipartite entanglement measure based on the geometric method. This measure arrives at the maximal value for the absolutely maximally entangled states and has desirable properties for quantifying…
We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…
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…
When a subset of particles in an entangled state is measured, the state of the subset of unmeasured particles is determined by the outcome of the measurement. This first measurement may be thought of as a state preparation for the remaining…
The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions. They are based on the trace norm of…
In the context of quantifying entanglement we study those functions of a multipartite state which do not increase under the set of local transformations. A mathematical characterization of these monotone magnitudes is presented. They are…
A multipartite entanglement measure called the ent is presented and shown to be an entanglement monotone, with the special property of automatic normalization. Necessary and sufficient conditions are developed for constructing maximally…
A Gaussian degree of entanglement for a symmetric two-mode Gaussian state can be defined as its distance to the set of all separable two-mode Gaussian states. The principal property that enables us to evaluate both Bures distance and…
The sliced Wasserstein distance as well as its variants have been widely considered in comparing probability measures defined on $\mathbb R^d$. Here we derive the notion of sliced Wasserstein distance for measures on an infinite dimensional…
We address the question of how much entanglement can be certified from the observed correlations and the knowledge of the Hilbert space dimension of the measured systems. We focus on the case in which both systems are known to be qubits.…
The relation between the violation of the Bell-CHSH inequalities and entanglement properties of quantum states is not clear so one may consider the mixedness of the system to understand the entanglement properties better than the Bell-CHSH…
Entanglement is generally considered necessary for achieving the Heisenberg limit in quantum metrology. We construct analogues of Dicke and GHZ states on a single $N+1$ dimensional qudit that achieve precision equivalent to symmetrically…
We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different…
Quantum entanglement is the quantum information processing resource. Thus it is of importance to understand how much of entanglement particular quantum states have, and what kinds of laws entanglement and also transformation between…
We propose an operational measure of distance of two quantum states, which conversely tells us their closeness. This is defined as a sum of differences in partial knowledge over a complete set of mutually complementary measurements for the…