Reconsidering Rapid Qubit Purification by Feedback

This paper reconsiders the claimed rapidity of a scheme for the purification of the quantum state of a qubit, proposed recently in Jacobs 2003 Phys. Rev. A67 030301(R). The qubit starts in a completely mixed state, and information is obtained by a continuous measurement. Jacobs' rapid purification protocol uses Hamiltonian feedback control to maximise the average purity of the qubit for a given time, with a factor of two increase in the purification rate over the no-feedback protocol. However, by re-examining the latter approach, we show that it mininises the average time taken for a qubit to reach a given purity. In fact, the average time taken for the no-feedback protocol beats that for Jacobs' protocol by a factor of two. We discuss how this is compatible with Jacobs' result, and the usefulness of the different approaches.Comment: 11 pages, 3 figures. Final version, accepted for publication in New J. Phy

Adiabatic Elimination in Compound Quantum Systems with Feedback

Feedback in compound quantum systems is effected by using the output from one sub-system (``the system'') to control the evolution of a second sub-system (``the ancilla'') which is reversibly coupled to the system. In the limit where the ancilla responds to fluctuations on a much shorter time scale than does the system, we show that it can be adiabatically eliminated, yielding a master equation for the system alone. This is very significant as it decreases the necessary basis size for numerical simulation and allows the effect of the ancilla to be understood more easily. We consider two types of ancilla: a two-level ancilla (e.g. a two-level atom) and an infinite-level ancilla (e.g. an optical mode). For each, we consider two forms of feedback: coherent (for which a quantum mechanical description of the feedback loop is required) and incoherent (for which a classical description is sufficient). We test the master equations we obtain using numerical simulation of the full dynamics of the compound system. For the system (a parametric oscillator) and feedback (intensity-dependent detuning) we choose, good agreement is found in the limit of heavy damping of the ancilla. We discuss the relation of our work to previous work on feedback in compound quantum systems, and also to previous work on adiabatic elimination in general.Comment: 18 pages, 12 figures including two subplots as jpeg attachment

All-optical versus electro-optical quantum-limited feedback

All-optical feedback can be effected by putting the output of a source cavity through a Faraday isolator and into a second cavity which is coupled to the source cavity by a nonlinear crystal. If the driven cavity is heavily damped, then it can be adiabatically eliminated and a master equation or quantum Langevin equation derived for the first cavity alone. This is done for an input bath in an arbitrary state, and for an arbitrary nonlinear coupling. If the intercavity coupling involves only the intensity (or one quadrature) of the driven cavity, then the effect on the source cavity is identical to that which can be obtained from electro-optical feedback using direct (or homodyne) detection. If the coupling involves both quadratures, this equivalence no longer holds, and a coupling linear in the source amplitude can produce a nonclassical state in the source cavity. The analogous electro-optic scheme using heterodyne detection introduces extra noise which prevents the production of nonclassical light. Unlike the electro-optic case, the all-optical feedback loop has an output beam (reflected from the second cavity). We show that this may be squeezed, even if the source cavity remains in a classical state.Comment: 21 pages. This is an old (1994) paper, but one which I thought was worth posting because in addition to what is described in abstract it has: (1) the first formulation (to my knowledge) of quantum trajectories for an arbitrary (i.e. squeezed, thermal etc.) broadband bath; (2) the prediction of a periodic modification to the detuning and damping of an oscillator for the simplest sort of all-optical feedback (i.e. a mirror) as seen in the recent experiment "Forces between a Single Atom and Its Distant Mirror Image", P. Bushev et al, Phys. Rev. Lett. 92, 223602 (2004

Measuring measurement--disturbance relationships with weak values

Using formal definitions for measurement precision {\epsilon} and disturbance (measurement backaction) {\eta}, Ozawa [Phys. Rev. A 67, 042105 (2003)] has shown that Heisenberg's claimed relation between these quantities is false in general. Here we show that the quantities introduced by Ozawa can be determined experimentally, using no prior knowledge of the measurement under investigation --- both quantities correspond to the root-mean-squared difference given by a weak-valued probability distribution. We propose a simple three-qubit experiment which would illustrate the failure of Heisenberg's measurement--disturbance relation, and the validity of an alternative relation proposed by Ozawa

Retroactive quantum jumps in a strongly-coupled atom-field system

We investigate a novel type of conditional dynamic that occurs in the strongly-driven Jaynes-Cummings model with dissipation. Extending the work of Alsing and Carmichael [Quantum Opt. {\bf 3}, 13 (1991)], we present a combined numerical and analytic study of the Stochastic Master Equation that describes the system's conditional evolution when the cavity output is continuously observed via homodyne detection, but atomic spontaneous emission is not monitored at all. We find that quantum jumps of the atomic state are induced by its dynamical coupling to the optical field, in order retroactively to justify atypical fluctuations in ocurring in the homodyne photocurrent.Comment: 4 pages, uses RevTex, 5 EPS figure

Continuous quantum error correction via quantum feedback control

We describe a protocol for continuously protecting unknown quantum states from decoherence that incorporates design principles from both quantum error correction and quantum feedback control. Our protocol uses continuous measurements and Hamiltonian operations, which are weaker control tools than are typically assumed for quantum error correction. We develop a cost function appropriate for unknown quantum states and use it to optimize our state-estimate feedback. Using Monte Carlo simulations, we study our protocol for the three-qubit bit-flip code in detail and demonstrate that it can improve the fidelity of quantum states beyond what is achievable using quantum error correction when the time between quantum error correction cycles is limited.Comment: 12 pages, 6 figures, REVTeX; references fixe

Quantum optical waveform conversion

Currently proposed architectures for long-distance quantum communication rely on networks of quantum processors connected by optical communications channels [1,2]. The key resource for such networks is the entanglement of matter-based quantum systems with quantum optical fields for information transmission. The optical interaction bandwidth of these material systems is a tiny fraction of that available for optical communication, and the temporal shape of the quantum optical output pulse is often poorly suited for long-distance transmission. Here we demonstrate that nonlinear mixing of a quantum light pulse with a spectrally tailored classical field can compress the quantum pulse by more than a factor of 100 and flexibly reshape its temporal waveform, while preserving all quantum properties, including entanglement. Waveform conversion can be used with heralded arrays of quantum light emitters to enable quantum communication at the full data rate of optical telecommunications.Comment: submitte

State and dynamical parameter estimation for open quantum systems

Following the evolution of an open quantum system requires full knowledge of its dynamics. In this paper we consider open quantum systems for which the Hamiltonian is ``uncertain''. In particular, we treat in detail a simple system similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]: a radiatively damped atom driven by an unknown Rabi frequency $\Omega$ (as would occur for an atom at an unknown point in a standing light wave). By measuring the environment of the system, knowledge about the system state, and about the uncertain dynamical parameter, can be acquired. We find that these two sorts of knowledge acquisition (quantified by the posterior distribution for $\Omega$, and the conditional purity of the system, respectively) are quite distinct processes, which are not strongly correlated. Also, the quality and quantity of knowledge gain depend strongly on the type of monitoring scheme. We compare five different detection schemes (direct, adaptive, homodyne of the $x$ quadrature, homodyne of the $y$ quadrature, and heterodyne) using four different measures of the knowledge gain (Shannon information about $\Omega$, variance in $\Omega$, long-time system purity, and short-time system purity).Comment: 14 pages, 18 figure

There is no unmet requirement of optical coherence for continuous-variable quantum teleportation

It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. 87, 077903 (2001)] that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not `truly coherent'. Here I show that `true coherence' is always illusory, as the concept of absolute time on a scale beyond direct human experience is meaningless. A laser is as good a clock as any other, even in principle, and this objection to teleportation experiments is baseless.Comment: 6 pages, no figures, no equations, to be published in Journal of Modern Optics. This is a long version of quant-ph/0104004. I have not replaced that paper with this one because some authors have referenced that one approvingly who may feel differently about doing so to this versio