相关论文: Algebraic structures of multipartite quantum syste…
Multipartite entanglement is a natural generalization of bipartite entanglement, but is relatively poorly understood. In this paper, we develop tools to calculate a class of multipartite entanglement measures - known as multi-invariants -…
We use open quantum system techniques to construct one-parameter semigroups of positive maps and apply them to study the entanglement properties of a class of 16-dimensional density matrices, representing states of a 4x4 bipartite system.
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…
We show that multipartite mixed bipartite CC and CQ states are geometrically and topologically distinguished in the space of states. They are characterized by non-vanishing Euler-Poincar\'{e} characteristics on the topological side and by…
We examine bipartite and multipartite correlations within the construct of unitary orbits. We show that the set of product states is a very small subset of set of all possible states, while all unitary orbits contain classically correlated…
The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful $k$-separability criteria of mixed $n$-partite ($n\geq 3$) quantum states to detect $k$-nonseparable $n$-partite quantum states.…
Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators is…
The pairwise correlations in a multi-qubit state are quantified through a linear variant of relative entropy. In particular, we derive the explicit expressions of total, quantum and classical bipartite correlations. Two different…
With an easily applicable criterion based on permutation symmetries of (identically prepared) replicas of quantum states we identify distinct entanglement classes in high-dimensional multi- partite systems. The different symmetry properties…
We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given…
In this paper we present several multipartite quantum systems featuring the same type of genuine (tripartite) entanglement. Based on a geometric interpretation of the so-called $|W\rangle$ and $|GHZ\rangle$ states we show that the…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
Quantum engineering now allows to design and construct multi-qubit states in a range of physical systems. These states are typically quite complex in nature, with disparate, but relevant properties that include both single and multi-qubit…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
Genuine multipartite entanglement is of great importance in quantum information, especially from the experimental point of view. Nevertheless, it is difficult to construct genuine multipartite entangled states systematically, because the…
If a pure state of a multipartite quantum system is Borromean, that is, its density matrix becomes product after tracing out any its component then the initial state is product itself. This shows the essentially classical nature of…
Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
We introduce algebriac sets in the products of complex projective spaces for multipartite mixed states, which are independent of their eigenvalues and only measure the "position" of their eigenvectors, as their non-local invariants (ie.…
We study separability criteria in multipartite quantum systems of arbitrary dimensions by using the Bloch representation of density matrices. We first derive the norms of the correlation tensors and obtain the necessary conditions for…