相关论文: On construction of anticliques for non-commutative…
Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operators to be invertible are obtained; so that the main results in the…
We study when local reduced density operators, viewed as quantum marginals, can be assembled into a global quantum state with a prescribed Markov structure. The starting point is a canonical logarithmic construction $T(\mathcal R)$, the…
We introduce several classes of quantum combinatorial designs, namely quantum Latin squares, cubes, hypercubes and a notion of orthogonality between them. A further introduced notion, quantum orthogonal arrays, generalizes all previous…
Given a graph $G$ and a parameter $k$, the $k$-biclique problem asks whether $G$ contains a complete bipartite subgraph $K_{k,k}$. This is the most easily stated problem on graphs whose parameterized complexity is still unknown. We provide…
We introduce a non-backtracking Laplace operator for graphs and we investigate its spectral properties. With the use of both theoretical and computational techniques, we show that the spectrum of this operator captures several structural…
We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a…
We prove a real interpolation characterization for some non Euclidean H\"older spaces, built on the Lie structure induced by a class of ultra-parabolic Kolmogorov-type operators satisfying the H\"ormander condition. As a by-product we also…
By establishing relations between operators on compositions, we show that the posets of compositions arising from the right and left Pieri rules for noncommutative Schur functions can each be endowed with both the structure of dual graded…
We present new combinatorial objects, which we call grid-labelled graphs, and show how these can be used to represent the quantum states arising in a scenario which we refer to as the faulty emitter scenario: we have a machine designed to…
Quantum graph state is a special class of nonlocal state among multiple quantum particles, underpinning several nonclassical and promising applications such as quantum computing and quantum secret sharing. Recently, establishing quantum…
A new anticyclic operad Mould is introduced, on spaces of functions in several variables. It is proved that the Dendriform operad is an anticyclic suboperad of this operad. Many operations on the free Mould algebra on one generator are…
We investigate static quark anti-quark operators based on trial states formed from eigenvectors of the covariant three-dimensional lattice Laplace operator. We test the method by computing the static quark-anti-quark potential and comparing…
In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized…
Graph states are an elegant and powerful quantum resource for measurement based quantum computation (MBQC). They are also used for many quantum protocols (error correction, secret sharing, etc.). The main focus of this paper is to provide a…
We develop a measurement operator formalism to handle quantum nondemolition (QND) measurement induced entanglement generation between two atomic gases. We first derive how the QND entangling scheme reduces to a positive operator-valued…
This is the second report of our work on the construction of directed strongly regular graphs. In our previous work, we constructed a couple of infinite families of new directed strongly regular graphs on the sets of antiflags of partial…
This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of…
It has long been known that long-ranged entangled topological phases can be exploited to protect quantum information against unwanted local errors. Indeed, conditions for intrinsic topological order are reminiscent of criteria for faithful…
We construct quantum K-invariants in non-archimedean analytic geometry. Contrary to the classical approach in algebraic geometry via perfect obstruction theory, we build on our previous works on the foundations of derived non-archimedean…
We present an elementary construction of an uncountably chromatic graph without uncountable, infinitely connected subgraphs.