相关论文: Graph States and the Variety of Principal Minors

Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural…

In this work, we study the complexity of graph-state preparation. We consider general quantum algorithms consisting of Clifford operations acting on at most two qubits for graph-state preparations. We define the CZ-complexity of a graph…

Lie groups, and therefore Lie algebras, are fundamental structures in quantum physics that determine the space of possible trajectories of evolving systems. However, classification and characterization methods for these structures are often…

Distinguishing sets of quantum states shared by two parties using only local operations and classical communication measurements is a fundamental topic in quantum communication and quantum information theory. We introduce a graph-theoretic…

For fixed positive integers $n$ and $k$, the Kneser graph $KG_{n,k}$ has vertices labeled by $k$-element subsets of $\{1,2,\dots,n\}$ and edges between disjoint sets. Keeping $k$ fixed and allowing $n$ to grow, one obtains a family of…

We pick up a solvable ${\cal PT}-$symmetric quantum square well on an interval of $x \in := (-L,L)\mathbb{G}^{(2)}$ (with an $\alpha-$dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just…

The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can…

In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…

Given a real-analytic manifold M, a compact connected Lie group G and a principal G-bundle P -> M, there is a canonical `generalized measure' on the space A/G of smooth connections on P modulo gauge transformations. This allows one to…

Standard Bell inequalities hold when distant parties are not allowed to communicate. Barrett et al. found correlations from Pauli measurements on certain network graphs refute a local hidden variable (LHV) description even allowing some…

Measurement based quantum computing is preformed by adding non-Clifford measurements to a prepared stabilizer states. Entangling gates like CZ are likely to have lower fidelities due to the nature of interacting qubits, so when preparing a…

We investigate a graph-theoretic approach to the problem of distinguishing quantum product states in the fundamental quantum communication framework called local operations and classical communication (LOCC). We identify chordality as the…

We present a strong connection between quantum information and quantum permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups, and then show…

A continuous-time quantum random walk describes the motion of a quantum mechanical particle on an underlying graph. The graph itself is associated with a Hilbert space of dimension equal to the number of vertices. The dynamics of the walk…

Extending upon the observations of the emergence of quantum-like states from classical complex synchronized networks, this work adds mathematical rigor to the analysis of single Quantum-Like (QL) bits constructed by eigenvectors of the…

Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…

A set of Pauli stings is well characterized by the graph that encodes its commutatitivity structure, i.e., by its frustration graph. This graph provides a natural interface between graph theory and quantum information, which we explore in…

Let $m_GI$ denote the number of Laplacian eigenvalues of a graph $G$ in an interval $I$ and let $\alpha(G)$ denote the independence number of $G$. In this paper, we determine the classes of graphs that satisfy the condition…

We provide a new branching rule from the general linear group $GL_{2n}(\mathbb{C})$ to the symplectic group $Sp_{2n}(\mathbb{C})$ by establishing a simple algorithm which gives rise to a bijection from the set of semistandard tableaux of a…

We classify, up to local unitary equivalence, the set of $n$-qubit states that is stabilized by the diagonal subgroup of the local unitary group. We exhibit a basis for this set, parameterized by diagrams of nonintersecting chords…