Discrete Wigner functions and the phase space representation of quantum teleportation

We present a phase space description of the process of quantum teleportation for a system with an $N$ dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones. This function is useful to represent composite quantum system in phase space and to analyze situations where entanglement between subsystems is relevant (dimensionality of the space of states of each subsystem is arbitrary). We also describe how a direct tomographic measurement of this Wigner function can be performed.Comment: 8 pages, 1 figure, to appear in Phys Rev

Quantum properties of the codirectional three-mode Kerr nonlinear coupler

We investigate the quantum properties for the codirectional three-mode Kerr nonlinear coupler. We investigate single-, two- and three-mode quadrature squeezing, Wigner function and purity. We prove that this device can provide richer nonclassical effects than those produced by the conventional coupler, i.e. the two-mode Kerr coupler. We show that it can provide squeezing and the quadrature squeezing exhibiting leaf-revival-collapse phenomenon in dependence on the values of the interaction parameters. In contrast to the conventional Kerr coupler two different forms of cat states can be simultaneously generated in the waveguides. We deduce conditions required for the complete disentanglement between the components of the system.Comment: 23 pages, 6 figure

Quantum computers in phase space

We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples, such as the Fourier Transform and Grover's search, we examine the conditions for the existence of a direct correspondence between quantum and classical evolutions in phase space. Finally, we describe how to directly measure the Wigner function in a given phase space point by means of a tomographic method that, itself, can be interpreted as a simple quantum algorithm.Comment: 16 pages, 7 figures, to appear in Phys Rev

Recovering coherence from decoherence: a method of quantum state reconstruction

We present a feasible scheme for reconstructing the quantum state of a field prepared inside a lossy cavity. Quantum coherences are normally destroyed by dissipation, but we show that at zero temperature we are able to retrieve enough information about the initial state, making possible to recover its Wigner function as well as other quasiprobabilities. We provide a numerical simulation of a Schroedinger cat state reconstruction.Comment: 8 pages, in RevTeX, 4 figures, accepted for publication in Phys. Rev. A (november 1999

Sampling functions for multimode homodyne tomography with a single local oscillator

We derive various sampling functions for multimode homodyne tomography with a single local oscillator. These functions allow us to sample multimode s-parametrized quasidistributions, density matrix elements in Fock basis, and s-ordered moments of arbitrary order directly from the measured quadrature statistics. The inevitable experimental losses can be compensated by proper modification of the sampling functions. Results of Monte Carlo simulations for squeezed three-mode state are reported and the feasibility of reconstruction of the three-mode Q-function and s-ordered moments from 10^7 sampled data is demonstrated.Comment: 12 pages, 8 figures, REVTeX, submitted Phys. Rev.

Quantum computing in optical microtraps based on the motional states of neutral atoms

We investigate quantum computation with neutral atoms in optical microtraps where the qubit is implemented in the motional states of the atoms, i.e., in the two lowest vibrational states of each trap. The quantum gate operation is performed by adiabatically approaching two traps and allowing tunneling and cold collisions to take place. We demonstrate the capability of this scheme to realize a square-root of swap gate, and address the problem of double occupation and excitation to other unwanted states. We expand the two-particle wavefunction in an orthonormal basis and analyze quantum correlations throughout the whole gate process. Fidelity of the gate operation is evaluated as a function of the degree of adiabaticity in moving the traps. Simulations are based on rubidium atoms in state-of-the-art optical microtraps with quantum gate realizations in the few tens of milliseconds duration range.Comment: 11 pages, 7 figures, for animations of the gate operation, see http://www.itp.uni-hannover.de/~eckert/na/index.htm

Quantum inference of states and processes

The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states provided that measurements on probe and transformed probe states are available. Drawbacks of various approximate treatments are considered.Comment: 7 pages, 4 figure

Quantum phase gate with a selective interaction

We present a proposal for implementing quantum phase gates using selective interactions. We analize selectivity and the possibility to implement these gates in two particular systems, namely, trapped ions and Cavity QED.Comment: Four pages of TEX file and two EPS figures. Submitted for publicatio

Self-homodyne tomography of a twin-beam state

A self-homodyne detection scheme is proposed to perform two-mode tomography on a twin-beam state at the output of a nondegenerate optical parametric amplifier. This scheme has been devised to improve the matching between the local oscillator and the signal modes, which is the main limitation to the overall quantum efficiency in conventional homodyning. The feasibility of the measurement is analyzed on the basis of Monte-Carlo simulations, studying the effect of non-unit quantum efficiency on detection of the correlation and the total photon-number oscillations of the twin-beam state.Comment: 13 pages (two-column ReVTeX) including 21 postscript figures; to appear on Phys. Rev.

Conditional large Fock state preparation and field state reconstruction in Cavity QED

We propose a scheme for producing large Fock states in Cavity QED via the implementation of a highly selective atom-field interaction. It is based on Raman excitation of a three-level atom by a classical field and a quantized field mode. Selectivity appears when one tunes to resonance a specific transition inside a chosen atom-field subspace, while other transitions remain dispersive, as a consequence of the field dependent electronic energy shifts. We show that this scheme can be also employed for reconstructing, in a new and efficient way, the Wigner function of the cavity field state.Comment: 4 Revtex pages with 3 postscript figures. Submitted for publicatio