Related papers: Geometrical structures of multipartite quantum sys…
This paper presents a new measure of entanglement which can be employed for multipartite entangled systems. The classification of multipartite entangled systems based on this measure is considered. Two approaches to applying this measure to…
In this review paper I present two geometric constructions of distinguished nature, one is over the field of complex numbers $\mathbb{C}$ and the other one is over the two elements field $\mathbb{F}_2$. Both constructions have been employed…
Multivariate (MTV) porous materials exhibit unique structural complexities based on diverse spatial arrangements of multiple building block combinations. These materials possess potential synergistic functionalities that exceed the sum of…
Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other, and then are entangled in the…
Entanglement is a unique nature of quantum theory and has tremendous potential for application. Nevertheless, the complexity of quantum entanglement grows exponentially with an increase in the number of entangled particles. Here we…
After recalling briefly some basic properties of the quantum group $GL_q(2)$, we study the quantum sphere $S_q^2$, quantum projective space $CP_q(N)$ and quantum Grassmannians as examples of complex (K\"{a}hler) quantum manifolds. The…
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 derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our…
We derive hierarchies of separability criteria that identify the different degrees of entanglement ranging from bipartite to genuine multi-partite in mixed quantum states of arbitrary size.
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
We construct a generalized controlled phased gate entangler for a multi-qubit state based on the geometrical structure of quantum systems. We also investigate relation between the generalized controlled phase construction of a quantum gate…
We review some concepts and properties of quantum correlations, in particular multipartite measures, geometric measures and monogamy relations. We also discuss the relation between classical and total correlations
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
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…
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…
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),…
The quantum deformation $CP_q(N)$ of complex projective space is discussed. Many of the features present in the case of the quantum sphere can be extended. The differential and integral calculus is studied and $CP_q(N)$ appears as a quantum…