Related papers: Entanglement and quantum combinatorial designs
There are many different classifications of entanglement for multipartite quantum systems, one of which is based on the number of unentangled particles. In this paper, we mainly study the quantum states containing at most $k-1$ unentangled…
We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the…
We investigate a new class of entangled states, which we call 'hyperentangled',that have EPR correlations identical to those in the vacuum state of a relativistic quantum field. We show that whenever hyperentangled states exist in any…
The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that t he classical-quantum correspondences such as encodings can be treated as dia gonal (d-)…
The unambiguous detection and quantification of entanglement is a hot topic of scientific research, though it is limited to low dimensions or specific classes of states. Here we identify an additional class of quantum states, for which…
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.…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
In this paper we consider the notion of quantum entanglement from the perspective of the logos categorical approach [26, 27]. Firstly, we will argue that the widespread distinctions, on the one hand, between pure states and mixed states,…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…
High-dimensional entanglement is a valuable resource for quantum communication, and photon pairs entangled in orbital angular momentum are commonly used for encoding high-dimensional quantum states. However, methods for preparation of…
The restrictions that nature places on the distribution of correlations in a multipartite quantum system play fundamental roles in the evolution of such systems, and yield vital insights into the design of protocols for the quantum control…
In this paper, after some recalls about connectivity structures and about the formalisms of quantum mechanics, we associate some families of connectivity structures with any entangled quantum state, and with any "measurement device" on such…
Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary…
Mixed state quantum computation can perform certain tasks which are believed to be efficiently intractable on a classical computer. For a specific model of mixed state quantum computation, namely, {\it deterministic quantum computation with…
The quantum entanglement as one of very important resources has been widely used in quantum information processing. In this work, we present a new kind of genuine multipartite entanglement. It is derived from special geometric feature of…
Ordering and classifying multipartite quantum states by their entanglement content remains an open problem. One class of highly entangled states, useful in quantum information protocols, the absolutely maximally entangled (AME) ones, are…
We propose a new classification scheme for quantum entanglement based on topological links. This is done by identifying a non-rigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the…
k-uniform mixed states are a significant class of states characterized by all k-party reduced states being maximally mixed. Novel methodologies are constructed for constructing k-uniform mixed states with the highest possible purity. By…
One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed…