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We investigate the use of continuously-applied external fields to maximize the fidelity of quantum logic operations performed on a decohering qubit. Assuming a known error operator and an environment represented by a scalar boson field at a finite temperature, we show how decoherence during logical operations can be efficiently reduced by applying a superposition of two external vector fields: one rotating orthogonally to the direction of the other, which remains static. The required field directions, frequency of rotation and amplitudes to decouple noise dynamically are determined by the coupling constants and the desired logical operation. We illustrate these findings numerically for a Hadamard quantum gate and an environment with ohmic spectral density.A quantum computer, when finally built, will be more efficient than current classical computers to solve certain kinds of problems [1]. The theory of quantum information processing generally takes advantage of the inherent parallelism exhibited by unitary operations on quantumstate superpositions. The terms of these linear combinations are tensor products of quantum bits, or "qubits" [2], which, linearly superposed, result in states with the desired properties of entanglement and interference [3]. In principle, the choice of an appropriate external field would guarantee a correct dynamics for the system, selected among those exhibiting unitary symmetry. However, during the actual quantum evolution of the system, since it cannot be completely separated from its environment, the unitary symmetry breaks down. The consequent decay of the quantum state purity is a manifestation of the ubiquitous phenomenon of decoherence [4].There are at least three major classes of strategic devices proposed to counteract the deleterious and unavoidable effects of decoherence: quantum error correcting codes [5], decoherence-free subspaces and subsystems [6], and dynamical decoupling [7,8,9,10]. Because the first two of these strategies require more than one physical qubit to protect each logical qubit, dynamical decoupling is the simplest of the three, since it requires, in principle, only controllable external fields to directly protect each physical qubit. Even without precise knowledge of the error structure and strengths, the pulsed dynamicaldecoupling scheme is effective, but usually employ an articulate time sequence of external-field pulses which, for experimental implementations, requires sophisticated control procedures. Moreover, the pulses have to be so short as to start and finish well within the environmental correlation time interval, so the field intensities involved must be high. Initial attempts to use continuously- * Electronic address: felipe@ifsc.usp.br applied fields instead of pulses have appeared recently [11] and these preliminary analyses show that, although pulses are not necessary for protecting against the effects of particular error structures assumed known, employing fast control cycles is inevitable. From the practical point of view of experimental rea...

We propose an alternative fidelity measure ͑namely, a measure of the degree of similarity͒ between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of Jozsa's axioms. The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.

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Three-dimensional quantum scattering calculations predict that the degree of optical shielding of cold collisions saturates with increasing intensity very differently from two-state models and is sensitive to the polarization of the shielding light. We report measurements showing how suppression of Na photoassociative ionization (PAI) rates is sensitive to the intensity and polarization of the shielding laser. At higher intensities, circular polarization suppresses PAI rates an order of magnitude more effectively than linear polarization, in qualitative agreement with our model calculations. PACS numbers: 32.80.Pj, 33.80.Ps, 34.50.Rk, 34.80.Qb The recently developed ability to optically cool and confine atoms [1] has opened the door to a new regime of ultracold collision processes [2][3][4] in which the frequency and intensity of externally applied fields can be used to switch on or turn off inelastic channels. The suppression of inelastic collision rates by optical shielding of ultracold, trapped atoms has been demonstrated experimentally [5][6][7][8][9] and calculated theoretically with two-state models [5,10]. In the shielding process, a blue detuned laser excites a repulsive state of the colliding atoms and causes the approaching atoms to turn around and separate, never getting closer together than the Condon point R C , where the quasimolecular system is in resonance with the light. In this way, the rate of an inelastic collision process due to interactions at much shorter range than R C can be strongly diminished. Shielding is important to investigate, since it can turn off "bad" collisions which lead to the loss of trapped atoms, while, in principle, minimizing heating due to excited state production [10,11]. Although the shielding phenomenon has been semiquantitatively explained by two-state Landau-Zener (LZ) models [5,10,11], these models are greatly oversimplified and can be misleading.In order to obtain a more realistic understanding of the optical shielding, we have carried out an exact threedimensional quantum scattering calculation for a simplified model problem of the collision in a strong radiation field [12]. Our calculations predict very different qualitative variation with increasing light intensity from existing two-state models, due to the role of multiphoton processes which couple different relative angular momentum states of the colliding ground state atoms via their mutual coupling through the excited state. As intensity increases, these differences are as follows: (1) greatly reduced shielding and greatly increased excited state production compared to LZ models, and (2) a strong polariza-tion dependence in these effects. The reduced shielding is consistent with observations on metastable Xe [8,13].Here we describe new observations on trapped Na which confirm our prediction that the optical shielding mechanism itself is sensitive to the polarization of the light field. At low intensities, below saturation, shielding can be interpreted in terms of the LZ avoided-crossing model that is in...

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.

We present a calculation of the fidelity of a cavity-field state teleported by means of a scheme that requires only two high-Q cavities. Based on current experimental capabilities, we demonstrate the feasibility of our scheme if the mean photon number of the cavity field is on the order of unity, allowing a reasonably accurate teleportation.PACS number͑s͒: 03.65. Bz, 03.67.Ϫa, 32.80.Rm, 42.50.Dv Quantum nonlocality has recently become the cornerstone of a set of striking proposals, which open the way to new quantum technologies: bit commitment ͓1͔, teleportation ͓2͔, computation ͓3͔, and communication ͓4͔. Inspired by these theoretical advances, experimentalists have developed techniques for the realization of teleportation ͓5͔ and to demonstrate quantum logic operations ͓6͔. However, the realization of all these proposals faces a crucial problem, intrinsic to the nature of entanglement: the decoherence of quantum states subjected to the action of the environment. This drastic process, transforming superpositions of quantum states into statistical mixtures, has been discussed by a number of authors ͓7,13͔ and, recently, observed experimentally ͓14͔. Since the coherence decays with a lifetime proportional to the inverse of the system excitation number ͓7͔, it becomes indispensable to estimate, from a given superposition, the fidelity of a resulting process. Recently, Braunstein and Kimble ͓8͔ have computed the fidelity of a teleported ''Schrödinger cat''-like state ͑SCLS͒ generated by parametric down-conversion as a running wave. Here, however, we focus on the specific problems of quantum-state engineering and teleportation in cavity quantum electrodynamics ͑CQED͒. In this realm, a SCLS teleportation protocol has recently been proposed, requiring three high-Q cavities ͓9͔. In the present paper, we advance computation of the fidelity of a trapped SCLS, teleported through a scheme based on only two high-Q cavities, whose feasibility we also analyze. The advantage of adopting our two-cavity scheme for teleporting a SCLS, as opposed to its alternative one in the literature ͓9͔, is twofold: it minimizes field dissipation through cavity damping mechanisms and also provides topological simplification of the experimental setup.Previously presented two-cavity schemes ͓10,11͔ have not envisaged teleportation of mesoscopic field states. In this work, the quantum channel employing a mixed atomic-field state, prepared through the interaction between a two-level atom and a cavity field, is more suitable to mesoscopic-state teleportation. Teleportation of N(Ͼ2)-dimensional states has also been proposed in the CQED domain ͓12͔.The teleportation apparatus is depicted in Fig. 1. The SCLS engineering consists of a two-level Rydberg atom A that crosses a Ramsey-type arrangement, i.e., a high-Q micromaser cavity C 1 located between two Ramsey zones R 1 and R 2 . After interacting with this arrangement, the atom is counted by detector D A , projecting the SCLS in C 1 . Subse-quently, this SCLS is teleported from Alice's cavity C 1 t...