Related papers: Optimal Measurements of Spin Direction
Measurement of quantum systems inevitably involves disturbance in various forms. Within the limits imposed by quantum mechanics, however, one can design an "ideal" projective measurement that does not introduce a back action on the measured…
We investigate four partial orderings on the space of quantum measurements (i.e on POVMs or positive operator valued measures), describing four notions of coarse/fine-ness of measurement. These are the partial orderings induced by: (1)…
We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and…
The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Over the last decade, many applications of the inverse Ising problem have arisen,…
This paper reviews quantum spin squeezing, which characterizes the sensitivity of a state with respect to an SU(2) rotation, and is significant for both entanglement detection and high-precision metrology. We first present various…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…
An important task for quantum information processing is optimal discrimination between two non-orthogonal quantum states, which until now has only been realized optically. Here, we present and compare experimental realizations of optimal…
The momentum changes caused by position measurements are a central feature of wave-particle duality. Here we investigate two cases - localization by a single slit, and which-way detection in the double-slit interference experiment - and…
The dependence of the particle rotation frequency on the particle orbit perturbations is found. The exact equation of spin motion in the cylindrical coordinate system is derived. The calculated formula for the frequency of g-2 precession is…
We analyze the optimal measurements accessing classical correlations in arbitrary two-qubit states. Two-qubit states can be transformed into the canonical forms via local unitary operations. For the canonical forms, we investigate the…
We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the…
Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…
With the example of a Stern-Gerlach measurement on a spin-1/2 atom, we show that a superposition of both paths may be observed compatibly with properties attributed to state collapse - for example, the singleness (or mutual exclusivity) of…
It is shown that the full unknown state of a spin-1/2 system, S, which, within Born's statistical interpretation, is meant as the state of an ensamble of identically prepared systems, can be determined with a simultaneous measurement with…
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…
From the point of view of the information theory, a model of the collapse phenomena at the measurement of a spin 1/2 projection is developed. This model phenomenologically includes an observer. The model allows not only to determine the…
Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state…
Recent advances in transmission electron microscopy (TEM) have opened the path toward spin resonance spectroscopy with single-spin sensitivity. To assess this potential, we investigate the quantum precision limits for sensing magnetic…
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model…