Related papers: Using a proxy state to improve the accuracy of tru…
We study different techniques that allow us to gain complete knowledge about an unknown quantum state, e.g. to perform full tomography of this state. We focus on two apparently simple cases, full tomography of one and two qubit systems. We…
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…
Quantum processes involving single-photon states are of broad interest in particular for quantum communication. Extending to continuous values a recent proposal by Yuan et al \cite{YUAN16}, we show that single-photon quantum processes can…
The procedure of extracting the ground-state parameters from vacuum-to-vacuum and vacuum-to-hadron correlators within the method of sum rules is considered. The emphasis is laid on the crucial ingredient of this method - the effective…
The quasidistributions corresponding to the diagonal representation of quantum states are discussed within the framework of operator-symbol construction. The tomographic-probability distribution describing the quantum state in the…
High precision multipole polarizabilities, $\alpha_{\ell}$ for $\ell \le 4$ of the $1s$ ground state of the hydrogen isoelectronic series are obtained from the Dirac equation using the B-spline method with Notre Dame boundary conditions.…
We discuss the concept of connection states (or connection matrices) that describe posterior ensembles, post-selected according to the outcomes of a quantum measurement. Connection matrices allow one to obtain results of any weak and some…
To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
We propose a scalable method for implementing linear optics quantum computation using the ``linked-state'' approach. Our method avoids the two-dimensional spread of errors occurring in the preparation of the linked-state. Consequently, a…
In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…
The accuracy of rate constants calculated using transition state theory depends crucially on the correct identification of a recrossing--free dividing surface. We show here that it is possible to define such optimal dividing surface in…
We present an efficient Monte Carlo algorithm for determining the density of states which is based on the statistics of transition probabilities between states. By measuring the infinite temperature transition probabilities--that is, the…
Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on…
A direct and exact method for calculating the density of states for systems with localized potentials is presented. The method is based on explicit inversion of the operator $E-H$. The operator is written in the discrete variable…
Accurately estimating the overlap between quantum states is a fundamental task in quantum information processing. While various strategies using distinct quantum measurements have been proposed for overlap estimation, the lack of…
Are there consistent and physically reasonable alternatives to the projection postulate? Does it have unique properties compared with acceptable alternatives? We answer these questions by systematically investigating hypothetical…
Puzzled or surprised by the almost incredible accuracy occasionally claimed in the literature to be achievable for numerical outcomes of QCD sum-rule analyses, we scrutinized the usual procedure employed for the extraction of the parameters…
The resonant state expansion, a rigorous perturbation theory, recently developed in electrodynamics, is applied to non-relativistic quantum mechanical systems in one dimension. The method is used here for finding the resonant states in…
Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary…