Quantum Measurements With a Quantum Computer

We present a scheme in which an ion trap quantum computer can be used to make arbitrarily accurate measurements of the quadrature phase variables for the collective vibrational motion of the ion. The electronic states of the ion become the 'apparatus', and the method is based on regarding the 'apparatus' as a quantum computer register which can be prepared in appropriate states by running a Fourier transform algorithm on the data stored within it. The resolution of the measurement rises exponentially with the number of ions used

Measurements on trapped laser-cooled ions using quantum computations

We show that a series of quantum computations involving an isolated N-quantum-bit ion register can be used to make an approximate quantum nondemolition measurement of the number state distribution of a collective vibrational mode. A unitary transformation is applied to the Fourier transformed state of the ion register to copy the vibrational statistics to the electronic mode, and the number state distribution is then measured in the electronic number state basis using the quantum jumps technique

Decoherence and robustness of parity-dependent entanglement in the dynamics of a trapped ion

We study the entanglement between the 2D vibrational motion and two ground state hyperfine levels of a trapped ion, Under particular conditions this entanglement depends on the parity of the total initial vibrational quanta. We study the robustness of this quantum coherence effect with respect to the presence of non-dissipative sources of decoherence, and of an imperfect initial state preparation.Comment: 13 pages, 5 figure

Beyond the Standard "Marginalizations" of Wigner Function

We discuss the problem of finding "marginal" distributions within different tomographic approaches to quantum state measurement, and we establish analytical connections among them.Comment: 12 pages, LaTex, no figures, to appear in Quantum and Semiclass. Op

Constant-time solution to the Global Optimization Problem using Bruschweiler's ensemble search algorithm

A constant-time solution of the continuous Global Optimization Problem (GOP) is obtained by using an ensemble algorithm. We show that under certain assumptions, the solution can be guaranteed by mapping the GOP onto a discrete unsorted search problem, whereupon Bruschweiler's ensemble search algorithm is applied. For adequate sensitivities of the measurement technique, the query complexity of the ensemble search algorithm depends linearly on the size of the function's domain. Advantages and limitations of an eventual NMR implementation are discussed.Comment: 14 pages, 0 figure

Quantum mechanical counterpart of nonlinear optics

Raman-type laser excitation of a trapped atom allows one to realize the quantum mechanical counterpart of phenomena of nonlinear optics, such as Kerr-type nonlinearities, parametric amplification, and multi-mode mixing. Additionally, huge nonlinearities emerge from the interference of the atomic wave function with the laser waves. They lead to a partitioning of the phase space accompanied by a significantly different action of the time evolution in neighboring phase-space zones. For example, a nonlinearly modified coherent "displacement" of the motional quantum state may induce strong amplitude squeezing and quantum interferences.Comment: 6 pages, 4 figures, to be published in Phys. Rev. A 55 (June

Generation of mesoscopic superpositions of two squeezed states of motion for a trapped ion

Published versio

Quantum Feedback Control: How to use Verification Theorems and Viscosity Solutions to Find Optimal Protocols

While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called "verification theorems" and "viscosity solutions" provide two useful tools for this purpose: together they give a simple method to check whether any given protocol is optimal, and provide a numerical method for finding optimal protocols. While treatments of verification theorems usually use sophisticated mathematical language, this is not necessary. In this article we give a simple introduction to feedback control in quantum systems, and then describe verification theorems and viscosity solutions in simple language. We also illustrate their use with a concrete example of current interest.Comment: 12 pages, revtex