Related papers: Tripartite connection condition for quantum graph …
We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
A systematic way of generating sets of local boundary conditions on the gauge fields in a path integral is presented. These boundary conditions are suitable for one--loop effective action calculations on manifolds with boundary and for…
The divergence condition is reformulated in the scaled boundary coordinates so as to prevent the spurious solutions in the finite element formulation.
Integrable open-boundary condition for the q-deformed Essler-Korepin-Schoutens extended Hubbard model of strongly correlated electrons, are studied in the framework of the boundary quantum inverse scattering method. Diagonal boundary…
We discuss approximations of the vertex coupling on a star-shaped quantum graph of $n$ edges in the singular case when the wave functions are not continuous at the vertex and no edge-permutation symmetry is present. It is shown that the…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
Quantum walk search may exhibit phenomena beyond the intuition from a conventional random walk theory. One of such examples is exceptional configuration phenomenon -- it appears that it may be much harder to find any of two or more marked…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
Quantification of quantum entanglement plays a crucial role in the study of quantum information tasks. We present analytical lower bounds for both concurrence and 2-concurrence based on the correlation matrices of bipartite quantum states.…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
Based on the standard transfer matrix, a formally exact quantization condition for arbitrary potentials, which outflanks and unifies the historical approaches, is derived. It can be used to find the exact bound-state energy eigenvalues of…
A third quantization formalism is applied to a simplified multiverse scenario. A well defined quantum state of the multiverse is obtained which agrees with standard boundary condition proposals. These states are found to be squeezed, and…
With the known group relations for the elements $(a,b,c,d)$ of a quantum matrix $T$ as input a general solution of the $RTT$ relations is sought without imposing the Yang - Baxter constraint for $R$ or the braid equation for $\hat{R} = PR$.…
We consider quantum search on graphs. Recently, it has been shown that the graph properties like connectivity, global symmetry, or regularity cannot serve as a reliable criteria that must be satisfied by a graph to allow a successful…
We study the concurrence of arbitrary dimensional bipartite quantum systems. An explicit analytical lower bound of concurrence is obtained, which detects entanglement for some quantum states better than some well-known separability…
In this paper, we study the concurrence of arbitrary dimensional tripartite quantum systems. An explicit operational lower bound of concurrence is obtained in terms of the concurrence of sub-states. A given example show that our lower bound…
A mixed quantum state is represented by a Hermitian positive semi-definite operator $\rho$ with unit trace. The positivity requirement is responsible for a highly nontrivial geometry of the set of quantum states. A known way to satisfy this…
We consider quantum graphs with spin-orbit couplings at the vertices. Time-reversal invariance implies that the bond S-matrix is in the orthogonal or symplectic symmetry class, depending on spin quantum number s being integer or…
We construct contact forms with constant $Q^\prime$-curvature on compact three-dimensional CR manifolds which admit a pseudo-Einstein contact form and satisfy some natural positivity conditions. These contact forms are obtained by…