Optimized monogamy and polygamy inequalities for multipartite qubit entanglement

We investigate the monogamy and polygamy inequalities of arbitrary multipartite quantum states, and provide new classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, and Tsallis-q entanglement, respectively. We show that these new monogamy and polygamy inequality relations are tighter than the existing ones with detailed examples.     

Tighter Weighted Polygamy Inequalities of Multipartite Entanglement in Arbitrary-Dimensional Quantum Systems

We investigate polygamy relations of multipartite entanglement in arbitrary-dimensional quantum systems. By improving an inequality and using the βth (0 ≤ β ≤ 1) power of entanglement of assistance, we provide a new class of weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems. We show that these new polygamy relations are tighter than the ones given in Kim (Phys. Rev. A 97, 042332 2018).

     

Hierarchical Polygamy Inequality for Entanglement of Tsallis q-Entropy

In this paper, we study the polygamy inequality of quantum entanglement in terms of Tsallis q-entropy.We first give a lower bound of Tsallis q-entropy entanglement of assistance(TOA) in the 2  d systems. The relationships between Tsallis q-entropy entanglement(TEE) and TOA are also given. Furthermore, we prove TOA follows a hierarchical polygamy inequality in a 2  2  2~(N-2) systems.     

Characterizing entanglement via uncertainty relations

We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a family of bound entangled states and true multipartite entangled states can be detected. The inequalities also allow us to distinguish between different classes of true tripartite entanglement for qubits. We formulate an equivalent criterion in terms of covariance matrices. This allows us to apply criteria known from the regime of continuous variables to finite-dimensional systems.     

Multipartite distribution property of one way discord beyond measurement

We investigate the distribution property of one way discord in the multipartite system by introducing the concept of polygamy deficit for one way discord. The difference between one way discord and quantum discord is analogue to the one between entanglement of assistance and entanglement of formation. For tripartite pure states, two kinds of polygamy deficits are presented with the equivalent expressions and physical interpretations regardless of measurement. For four-partite pure states, we provide a condition which makes one way discord polygamy satisfied. In addition, we generalize these results to the case for N$N$-partite pure states. Those results can be applicable to multipartite quantum systems and are complementary to our understanding of the shareability of quantum correlations.     

Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.     

Generation of Quantized Vortices in Multilayered Bose-Einstein Condensates

International Journal of Theoretical Physics - We study the monogamy and polygamy inequalities of quantum correlations in arbitrary dimensional multipartite quantum systems. We first derive the...     

Experimental detection of quantum entanglement

In this review, we introduce some methods for detecting or measuring entanglement. Several nonlinear entanglement witnesses are presented. We derive a series of Bell inequalities whose maximally violations for any multipartite qubit states can be calculated by using our formulas. Both the nonlinear entanglement witnesses and the Bell inequalities can be operated experimentally. Thus they supply an effective way for detecting entanglement. We also introduce some experimental methods to measure the entanglement of formation, and the lower bound of the convex-roof extension of negativity.     

Entanglement Conditions for Mixed SU(2) and SU(1, 1) Systems

We derive a class of inequalities for detecting entanglement in the mixed SU(2) and SU(1,?1) systems based on the Schrödinger-Robertson indeterminacy relations in conjugation with the partial transposition. These inequalities are in general stronger than those based on the usual Heisenberg uncertainty relations for detecting entanglement. Furthermore, based on the complete reduction from SU(2) and SU(1,?1) systems to bosonic systems, we derive some entanglement conditions for two-mode systems. We also use the partial reduction to obtain some inequalities in the mixed SU(2) (or SU(1,?1)) and bosonic systems.     

Continuous variable tripartite entanglement and Einstein-Podolsky-Rosen correlations from triple nonlinearities

We develop three-mode generalizations of the Einstein-Podolsky-Rosen paradox, allowing us to define inequalities which may be used to indicate continuous-variable tripartite entanglement. We use these inequalities and an appropriate version of the previously developed van Loock-Furusawa inequalities to theoretically compare the continuous-variable tripartite entanglement available from the use of three concurrent x ⁽²⁾ nonlinearities and from three independent squeezed states mixed on beamsplitters. The text was submitted by the authors in English.     

Lower Bounds on the Squashed Entanglement for Multi-Party System

Squashed entanglement is a promising entanglement measure that can be generalized to multipartite case, and it has all of the desirable properties for a good entanglement measure. In this paper we present computable lower bounds to evaluate the multipartite squashed entanglement. We also derive some inequalities relating the squashed entanglement to other entanglement measures.     

Nonlinear entanglement witnesses

Entanglement detection typically relies on linear inequalities for mean values of certain observables (entanglement witnesses), where violation indicates entanglement. We provide a general method to improve any of these inequalities for bipartite systems via nonlinear expressions. The nonlinearities are of different orders and can be directly measured in experiments, often without any extra effort.     

Generalized Entanglement Monogamy and Polygamy Relations for N-Qubit Systems

We investigate the generalized monogamy and polygamy relations N-qubit systems. We give a general upper bound of the αth (0 ≤ α ≤ 2) power of concurrence for N-qubit states. The monogamy relations satisfied by the αth (0 ≤ α ≤ 2) power of concurrence are presented for N-qubit pure states under the partition AB and C₁...C_N− 2, as well as under the partition ABC₁ and C₂⋯C_N− 2. These inequalities give rise to the restrictions on entanglement distribution and the trade off of entanglement among the subsystems. Similar results are also derived for negativity.

     

Spin squeezing inequalities for arbitrary spin

We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in an ensemble in which the particles cannot be individually addressed. We also present a large set of criteria involving collective observables different from the angular momentum coordinates. We show that some of the inequalities can be used to detect k-particle entanglement and bound entanglement.     

Spin squeezing inequalities and entanglement of N qubit states

We derive spin squeezing inequalities that generalize the concept of the spin squeezing parameter and provide necessary and sufficient conditions for genuine 2-, or 3-qubit entanglement for symmetric states, and sufficient condition for N-qubit states. Our inequalities have a clear physical interpretation as entanglement witnesses, can be easily measured, and are given by complex but elementary expressions.     

Bell inequalities for graph states

We investigate the nonlocal properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, for each graph state there is an inequality maximally violated only by that state. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement.     

Bell-type inequalities for partial separability in N-particle systems and quantum mechanical violations

We derive N-particle Bell-type inequalities under the assumption of partial separability, i.e., that the N-particle system is composed of subsystems which may be correlated in any way (e.g., entangled) but which are uncorrelated with respect to each other. These inequalities provide, upon violation, experi-mentally accessible sufficient conditions for full N-particle entanglement, i.e., for N-particle entanglement that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. The inequalities are shown to be maximally violated by the N-particle Greenberger-Horne-Zeilinger states.     

Impact of Distribution Fairness Degree and Entanglement Degree on Cooperation

We explore the impact of distributional fairness degree and entanglement degree on the cooperation between different players by investigating a modified prisoner's dilemma game. We not only introduce a new concept of distributional fairness degree, but also obtain the cooperation conditions for overcoming dilemma in terms of fairness and entanglement inequalities. It is demonstrated that distributional fairness can be of fundamental importance to promote cooperation with the help of quantum entanglement.     

Classification of 4-qubit Entangled Graph States According to Bipartite Entanglement,Multipartite Entanglement and Non-local Properties

We use concurrence to study bipartite entanglement, Meyer-Wallach measure and its generalizations to study multi-partite entanglement and MABK and SASA inequalities to study the non-local properties of the 4-qubit entangled graph states, quantitatively. Then, we present 3 classifications, each one in accordance with one of the aforementioned properties. We also observe that the classification according to multipartite entanglement does exactly coincide with that according to nonlocal properties, but does not match with that according to bipartite entanglement. This observation signifies the fact that non-locality and multipartite entanglement enjoy the same basic underlying principles, while bipartite entanglement may not reveal the non-locality issue in its entirety.