相关论文: On construction of anticliques for non-commutative…

We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras.…

We introduce a generalization of the notion of operad that we call a contractad, whose set of operations is indexed by connected graphs and whose composition rules are numbered by contractions of connected subgraphs. We show that many…

Non-classical states that are characterized by their non-positive quasi-probabilities in phase space are known to be the basis for various quantum effects. In this work, we investigate the interrelation between the non-classicality and…

We construct a noncommutative geometry with generalised `tangent bundle' from Fell bundle $C^*$-categories ($E$) beginning by replacing pair groupoid objects (points) with objects in $E$. This provides a categorification of a certain class…

A unified formalism was developed in [S. Adhikary et. al., arXiv:1710.04371 [quant-ph]], for describing non-classicality of states by introducing pseudo projection operators in which both quantum logic and quantum probability are naturally…

Graph states are well-entangled quantum states that are defined based on a graph. Of course, if two graphs are isomorphic their associated states are the same. Also, we know local operations do not change the entanglement of quantum states.…

Recently, a novel GHZ/W graphical calculus has been established to study and reason more intuitively about interacting quantum systems. The compositional structure of this calculus was shown to be well-equipped to sufficiently express…

Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…

We provide a graphical method to describe and analyze non-Gaussian quantum states using a hypergraph framework. These states are pivotal resources for quantum computing, communication, and metrology, but their characterization is hindered…

We give a general construction of extended moduli spaces of topological D-branes as non-commutative algebraic varieties. This shows that noncommutative symplectic geometry in the sense of Kontsevich arises naturally in String Theory.

Graph states are a fundamental class of multipartite entangled quantum states with wide-ranging applications in quantum information and computation. In this work, we develop a systematic framework for constructing and analyzing…

We construct a period mapping for deformations of a differential graded algebra, that generalizes Griffiths' period mapping. It is constructed as a morphism between differential graded Lie algebras which has a moduli-theoretic…

Graph states are quantum states that can be described by a stabilizer formalism and play an important role in quantum information processing. We consider the action of local unitary operations on graph states and hypergraph states. We focus…

In this paper, we propose a new way to represent graphs in quantum space. In that approach, we replace the rows of the adjacency matrix of the graph by state vectors in the occupation number representation. Unlike the traditional definition…

We introduce a formalism for derived moduli functors on differential graded associative algebras, which leads to non-commutative enhancements of derived moduli stacks and naturally gives rise to structures such as Hall algebras. Descent…

We put forward a simple construction of genuinely entangled subspaces -- subspaces supporting only genuinely multipartite entangled states -- of any permissible dimensionality for any number of parties and local dimensions. The method uses…

Higher-rank graph generalisations of the Popescu-Poisson transform are constructed, allowing us to develop a dilation theory for higher rank operator tuples. These dilations are joint dilations of the families of operators satisfying…

Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a…

For manipulations of multipartite quantum systems, it was well known that all local operations assisted by classical communication (LOCC) constitute a proper subset of the class of separable operations. Recently, Gheorghiu and Griffiths…

Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states and a generalization of the well--established notion of graph states. Mathematically, they can conveniently be described by a…