Entanglement In Multipartite Quantum Systems Research Articles

Continuity of the relative entropy of resource

We present a criterion to establish the local continuity of the relative entropy of resource, i.e. the relative entropy distance to the set of free states, in any quantum resource theory. Several basic corollaries of this criterion are presented. Applications to the relative entropy of entanglement in multipartite quantum systems are considered. It is shown, in particular, that local continuity of any relative entropy of multipartite entanglement follows from local continuity of the quantum mutual information.

Multipartite entanglement detection via generalized Wigner–Yanase skew information

The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory. In this paper, we investigate k-nonseparability and k-partite entanglement of N-partite quantum systems from the perspective of the generalized Wigner–Yanase skew information. We deduce the upper bounds on the generalized Wigner–Yanase skew information of k-separable states and k-producible states in arbitrary dimensional multipartite quantum systems. And based on the upper bounds, we develop two different approaches in form of simple inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner–Yanase skew information. Any violation of these inequalities by a quantum state reveals its k-nonseparability or k-partite entanglement, so these inequalities present the hierarchic classifications of k-nonseparability or k-partite entanglement for all N-partite quantum states from N-nonseparability to 2-nonseparability or from 2-partite entanglement to N-partite entanglement. Some well-known entanglement criteria are the special cases of our criteria. We illustrate the significance of our criteria by showing that they can reveal k-nonseparability and k-partite entanglement undetectable by well-known criteria through several typical examples, and their advantages over well-known criteria.

Tightening monogamy and polygamy relations of unified entanglement in multipartite systems

We study the monogamy and polygamy inequalities of unified entanglement in multipartite quantum systems. We first derive the monogamy inequality of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition, and then obtain the monogamy inequalities of the $\alpha$th ($0\leq\alpha\leq\frac{r}{2}, r\geq\sqrt{2}$) power of entanglement of formation for tripartite states and their generalizations in multi-qubit quantum states. We also generalize the polygamy inequalities of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition. Moreover, we investigate polygamy inequalities of the $\beta$th ($\beta\geq \max\{1, s\}, 0\leq s\leq s_0, 0\leq s_0\leq\sqrt{2}$) power of the entanglement of formation for $2\otimes2\otimes2$ and $n$-qubit quantum systems. Finally, using detailed examples, we show that the results are tighter than previous studies.

Nonlocality of tripartite orthogonal product states

Local distinguishability of orthogonal product states is an area of active research in quantum information theory. However, most of the relevant results about local distinguishability are found in bipartite quantum systems and very few are known in multipartite cases. In this paper, we construct a locally indistinguishable subset in $${\mathbb {C}}^{2d}\bigotimes {\mathbb {C}}^{2d}\bigotimes {\mathbb {C}}^{2d}$$ , $$d\ge 2$$ that contains $$18(d-1)$$ orthogonal product states. Further, we generalize our method to arbitrary tripartite quantum systems $${\mathbb {C}}^{k}\bigotimes {\mathbb {C}}^{l}\bigotimes {\mathbb {C}}^{m}$$ . This result helps us to understand the role of nonlocality without entanglement in multipartite quantum systems. Finally, we prove that a three-qubit GHZ state is sufficient as a resource to distinguish each of the above classes of states.

K-stretchability of entanglement, and the duality of k-separability and k-producibility

The notions of k-separability and k-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this work we reveal a partial duality between them, which is valid also for their correlation counterparts. This duality can be seen from a much wider perspective, when we consider the entanglement and correlation properties which are invariant under the permutations of the subsystems. These properties are labeled by Young diagrams, which we endow with a refinement-like partial order, to build up their classification scheme. This general treatment reveals a new property, which we call k-stretchability, being sensitive in a balanced way to both the maximal size of correlated (or entangled) subsystems and the minimal number of subsystems uncorrelated with (or separable from) one another.

Coarse-grained entanglement classification through orthogonal arrays

Classification of entanglement in multipartite quantum systems is an open problem solved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in systems consisting of N subsystems with an arbitrary number of internal levels each, based on the properties of orthogonal arrays with N columns. In particular, we investigate in detail a subset of highly entangled pure states which contains all states defining maximum distance separable codes. To illustrate the methods presented, we analyze systems of four and five qubits, as well as heterogeneous tripartite systems consisting of two qubits and one qutrit or one qubit and two qutrits.

Kind of entanglement that speeds up quantum evolution

The "speed" of unitary quantum evolution was recently shown to be connected to entanglement in multipartite quantum systems. Here, we discuss a tighter version of the Mandelstam-Tamm uncertainty relation that depends on the Fisher information. The passage time is estimated by a lower bound that depends inversely proportional to the square root of the Fisher information. This leads to a better understanding of the origin of a fast quantum time evolution of entangled states.

ENTANGLEMENT SHARING: FROM QUBITS TO GAUSSIAN STATES

It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such monogamy constraints have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In this paper we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of N qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.