Related papers: A Note on Parallel Distinguishability of two Quant…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary…
The development of quantum algorithms and protocols calls for adequate modelling and verification techniques, which requires abstracting and focusing on the basic features of quantum concurrent systems, like CCS and CSP have done for their…
We consider partial and total reduction of a nonhomogeneous linear system of the operator equations with the system matrix in the same particular form as in paper [N. Shayanfar, M. Hadizadeh 2013]. Here we present two different concepts.…
We derive the implications of particle-vortex duality for the electromagnetic response of Quantum Hall systems beyond the linear-response regime. This provides a first theoretical explanation of the remarkable duality which has been…
We are interested in looking for two nontrivial solutions for a class of nonhomogeneous quasilinear elliptic system with sign-changing weight functions and concave-convex nonlinearities on the bounded domain. This kind of quasilinear…
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…
We use the generalized concurrence approach to investigate the general multipartite separability problem. By extending the preconcurrence matrix formalism to arbitrary multipartite systems, we show that the separability problem can be…
We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
We give a careful proof that a parallelized version of adiabatic quantum computation can efficiently simulate universal gate model quantum computation. The proof specifies an explicit parameter-dependent Hamiltonian $H({\lambda})$ that is…
We prove a conjecture about the minimal nonnegative solutions of algebraic Riccati equations associated with reducible singular M-matrices. The result enhances our understanding of the behaviour of doubling algorithms for finding the…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
Let $A$ be a $C^{*}$ algebra and $T: A\rightarrow A$ be a linear map which satisfies the functional equation $\begin{cases}T(x)T(y)=T^{2}(xy)\\T(x^{*})=T(x)^{*} \end{cases}$ We prove that under each of the following conditions, $T$ must be…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
Given two systems $P=(P_j(D))_{j=1}^N$ and $Q=(Q_j(D))_{j=1}^M$ of linear partial differential operators with constant coefficients, we consider the spaces ${\mathcal E}_\omega^P$ and ${\mathcal E}_\omega^Q$ of $\omega$-ultradifferentiable…
Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining, machine learning, and network science. By…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…