Related papers: Algebraic structures of multipartite quantum syste…
Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…
First, we show how the quantum circuits for generating and measuring multi-party entanglement of qubits can be translated to continuous quantum variables. We derive sufficient inseparability criteria for $N$-party continuous-variable states…
The variety of multi-partite entangled states enables numerous applications in novel quantum information tasks. In order to compare the suitability of different states from a theoretical point of view classifications have been introduced.…
Multipartite entanglement is one of the crucial resources in quantum information processing tasks such as quantum metrology, quantum computing and quantum communications. It is essential to verify not only the multipartite entanglement, but…
We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
In the first part of this paper we analyze possible quantum computational capacities due to quantum queries associated with equi-partitions of pure orthogonal states. Special emphasis is given to the parity of product states and to…
Multipartite generalizations of spin coherent states are introduced and analyzed. These are the spin analogues of multimode optical coherent states as used in continuous variable quantum information, but generalized to possess full spin…
We introduce a general framework for detecting genuine multipartite entanglement and non full-separability in multipartite quantum systems of arbitrary dimensions based on correlation tensors. Regarding genuine multipartite entanglement our…
A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite…
One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
Topos quantum theory provides representations of quantum states as direct generalizations of the probability distribution, namely probability valuation. In this article, we consider extensions of a known bijective correspondence between…
We investigate genuine multipartite entanglement in general multipartite systems. Based on the norms of the correlation tensors of a multipartite state under various partitions, we present an analytical sufficient criterion for detecting…
Building upon the results of [R. Augusiak et al., Phys. Rev. Lett. 115, 030404 (2015)] we develop a general approach to the generation of genuinely entangled multipartite states of any number of parties from genuinely entangled states of a…
One of the key manifestations of quantum mechanics is the phenomenon of quantum entanglement. While the entanglement of bipartite systems is already well understood, our knowledge of entanglement in multipartite systems is still limited.…
This thesis is an attempt to enhance understanding of the following questions A- Given a multipartite quantum state (possibly mixed), how to find out whether it is entangled or separable? (Detection of entanglement.) B- Given an entangled…
We derive a general framework that connects every positive map with a corresponding witness for partial separability in multipartite quantum systems. We show that many previous approaches were intimately connected to the witnesses derived…
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.