相关论文: On beta pentagon relations
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
Description of two three-dimensional topological quantum field theories of Witten type as twisted supersymmetric theories is presented. Low-energy effective action and a corresponding topological invariant of three-dimensional manifolds are…
A quantum generalization of Rogers' five term, or ``pentagon'' dilogarithm identity is suggested. It is shown that the classical limit gives usual Rogers' identity. The case where the quantum identity is realized in finite dimensional space…
Consider three qubits A, B, and C which may be entangled with each other. We show that there is a trade-off between A's entanglement with B and its entanglement with C. This relation is expressed in terms of a measure of entanglement called…
Entanglement is one of important resources for quantum communication tasks. Most of results are focused on qubit entanglement. Our goal in this work is to characterize the multipartite high-dimensional entanglement. We firstly derive an…
Three-body Faddeev equations are considered as a spectral problem for nonsymmetrical matrix operator. Invariant subspaces related to physical and spurious solutions to Faddeev equations and its adjoint are described. Respective eigenvectors…
Quantum theory can be understood as pointing to an ontology of relations. I observe that this reading of quantum mechanics is supported by the ubiquity of relationality in contemporary fundamental physics, including in classical mechanics,…
We discuss the analogy between topological entanglement and quantum entanglement, particularly for tripartite quantum systems. We illustrate our approach by first discussing two clearly (topologically) inequivalent systems of three-ring…
The monogamy and polygamy properties of quantum entanglement characterize fundamental constraints on the distribution of entanglement in multipartite quantum systems. In this paper, we investigate tighter monogamy and polygamy relations for…
We point out that the q-entropy composition for independent events has exactly the same form as the Pythagorean theorem in hyperbolic geometry. We justify the formal relation of hyperbolic geometry with the q-entropy through the use of the…
The transactional interpretation of quantum mechanics, which uses retarded and advanced solutions of the Schrodinger equation and its complex conjugate, offers an original way to visualize and understand quantum processes. After a brief…
We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our…
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
New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…
Quantifying genuine entanglement is a crucial task in quantum information theory.In this work, we give an approach of constituting genuine $m$-partite entanglement measures from any bipartite entanglement and any $k$-partite entanglement…
The main subject of the paper is the pentagon relation. This relation can be expressed in different ways. We start with the natural geometric form of the pentagon relation. Then we express it in algebraic form as a family of equations with…
A theory of (co)homologies related to set-theoretic $n$-simplex relations is constructed in analogy with the known quandle and Yang--Baxter (co)homologies, with emphasis made on the tetrahedron case. In particular, this permits us to…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
The notion of entanglement is the most well-known nonclassical correlation in quantum mechanics and a fundamental resource in quantum information and computation. This correlation, which is displayed by certain classes of quantum states, is…
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…