Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension

Let p be an odd prime and let r be the smallest generator of the multiplicative group Zp∗. We show that there exists a correlation of size Θ(r2) that self-tests a maximally entangled state of local dimension p−1. The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. (2019)). Since there are infinitely many prime numbers whose smallest multiplicative generator is in the set {2,3,5} (D.R. Heath-Brown The Quarterly Journal of Mathematics (1986) and M. Murty The Mathematical Intelligencer (1988)), our result implies that constant-sized correlations are sufficient for self-testing of maximally entangled states with unbounded local dimension.

Greenberger–Horne–Zeilinger states: Their identifications and robust violations

The [Formula: see text]-qubit Greenberger–Horne–Zeilinger (GHZ) states are the maximally entangled states of [Formula: see text] qubits, which have had many important applications in quantum information processing, such as quantum key distribution and quantum secret sharing. Thus how to distinguish the GHZ states from other quantum states becomes a significant problem. In this work, by presenting a family of the generalized Clauser–Horne–Shimony–Holt (CHSH) inequality, we show that the [Formula: see text]-qubit GHZ states can be indeed identified by the maximal violations of the generalized CHSH inequality under some specific measurement settings. The generalized CHSH inequality is simple and contains only four correlation functions for any [Formula: see text]-qubit system, thus has the merit of facilitating experimental verification. Furthermore, we present a quantum phenomenon of robust violations of the generalized CHSH inequality in which the maximal violation of Bell’s inequality can be robust under some specific noises adding to the [Formula: see text]-qubit GHZ states.

Maximally Entangled SU(1,1) Semi Coherent States

In this paper, we consider a special type of maximally entangled states namely by entangled SU(1,1) semi coherent states by using SU(1,1) semi coherent states(SU(1,1) Semi CS). The entanglement characteristics of these entangled states are studied by evaluating the concurrence.We investigate some of their nonclassical properties,especially probability distribution function,second-order correlation function and quadrature squeezing . Further, the quasiprobability distribution functions (Q-functions) is discussed.

A complete hierarchy for the pure state marginal problem in quantum mechanics

Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state for some given marginals. This problem arises in many contexts, ranging from quantum chemistry to entanglement theory and quantum error correcting codes. In this paper, we prove a correspondence of the marginal problem to the separability problem. Based on this, we describe a sequence of semidefinite programs which can decide whether some given marginals are compatible with some pure global quantum state. As an application, we prove that the existence of multiparticle absolutely maximally entangled states for a given dimension is equivalent to the separability of an explicitly given two-party quantum state. Finally, we show that the existence of quantum codes with given parameters can also be interpreted as a marginal problem, hence, our complete hierarchy can also be used.

Bipartite entanglement of decohered mixed states generated from maximally entangled cluster states

In this work, we investigate the bipartite entanglement of decohered mixed states generated from maximally entangled cluster states of [Formula: see text] qubits physical system. We introduce the disconnected cluster states for an ensemble of [Formula: see text] non-interacting qubits and we give the corresponding separable density matrices. The maximally entangled states can be generated from disconnected cluster states, by assuming that the dynamics of the multi-qubit system is governed by a quadratic Hamiltonian of Ising type. When exposed to a local noisy interaction with the environment, the multi-qubit system evolves from its initial pure maximally entangled state to a decohered mixed state. The decohered mixed states generated from bipartite, tripartite and multipartite maximally entangled cluster states are explicitly expressed and their bipartite entanglements are investigated.