3,115 research outputs found
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
In-loop squeezing is real squeezing to an in-loop atom
Electro-optical feedback can produce an in-loop photocurrent with arbitrarily
low noise. This is not regarded as evidence of `real' squeezing because
squeezed light cannot be extracted from the loop using a linear beam splitter.
Here I show that illuminating an atom (which is a nonlinear optical element)
with `in-loop' squeezed light causes line-narrowing of one quadrature of the
atom's fluorescence. This has long been regarded as an effect which can only be
produced by squeezing. Experiments on atoms using in-loop squeezing should be
much easier than those with conventional sources of squeezed light.Comment: 4 pages, 2 figures, submitted to PR
Decoherence and the conditions for the classical control of quantum systems
We find the conditions for one quantum system to function as a classical
controller of another quantum system: the controller must be an open system and
rapidly diagonalised in the basis of the controller variable that is coupled to
the controlled system. This causes decoherence in the controlled system that
can be made small if the rate of diagonalisation is fast. We give a detailed
example based on the quantum optomechanical control of a mechanical resonator.
The resulting equations are similar in structure to recently proposed models
for consistently combining quantum and classical stochastic dynamics
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
Entanglement under restricted operations: Analogy to mixed-state entanglement
We show that the classification of bi-partite pure entangled states when
local quantum operations are restricted yields a structure that is analogous in
many respects to that of mixed-state entanglement. Specifically, we develop
this analogy by restricting operations through local superselection rules, and
show that such exotic phenomena as bound entanglement and activation arise
using pure states in this setting. This analogy aids in resolving several
conceptual puzzles in the study of entanglement under restricted operations. In
particular, we demonstrate that several types of quantum optical states that
possess confusing entanglement properties are analogous to bound entangled
states. Also, the classification of pure-state entanglement under restricted
operations can be much simpler than for mixed-state entanglement. For instance,
in the case of local Abelian superselection rules all questions concerning
distillability can be resolved.Comment: 10 pages, 2 figures; published versio
Decoherence-full subsystems and the cryptographic power of a private shared reference frame
We show that private shared reference frames can be used to perform private
quantum and private classical communication over a public quantum channel. Such
frames constitute a novel type of private shared correlation (distinct from
private classical keys or shared entanglement) useful for cryptography. We
present optimally efficient schemes for private quantum and classical
communication given a finite number of qubits transmitted over an insecure
channel and given a private shared Cartesian frame and/or a private shared
reference ordering of the qubits. We show that in this context, it is useful to
introduce the concept of a decoherence-full subsystem, wherein every state is
mapped to the completely mixed state under the action of the decoherence.Comment: 13 pages, published versio
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 (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 , 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
quadrature, homodyne of the quadrature, and heterodyne) using four
different measures of the knowledge gain (Shannon information about ,
variance in , long-time system purity, and short-time system purity).Comment: 14 pages, 18 figure
Adaptive single-shot phase measurements: The full quantum theory
The phase of a single-mode field can be measured in a single-shot measurement
by interfering the field with an effectively classical local oscillator of
known phase. The standard technique is to have the local oscillator detuned
from the system (heterodyne detection) so that it is sometimes in phase and
sometimes in quadrature with the system over the course of the measurement.
This enables both quadratures of the system to be measured, from which the
phase can be estimated. One of us [H.M. Wiseman, Phys. Rev. Lett. 75, 4587
(1995)] has shown recently that it is possible to make a much better estimate
of the phase by using an adaptive technique in which a resonant local
oscillator has its phase adjusted by a feedback loop during the single-shot
measurement. In Ref.~[H.M. Wiseman and R.B. Killip, Phys. Rev. A 56, 944] we
presented a semiclassical analysis of a particular adaptive scheme, which
yielded asymptotic results for the phase variance of strong fields. In this
paper we present an exact quantum mechanical treatment. This is necessary for
calculating the phase variance for fields with small photon numbers, and also
for considering figures of merit other than the phase variance. Our results
show that an adaptive scheme is always superior to heterodyne detection as far
as the variance is concerned. However the tails of the probability distribution
are surprisingly high for this adaptive measurement, so that it does not always
result in a smaller probability of error in phase-based optical communication.Comment: 17 pages, LaTeX, 8 figures (concatenated), Submitted to Phys. Rev.
Optimal states and almost optimal adaptive measurements for quantum interferometry
We derive the optimal N-photon two-mode input state for obtaining an estimate
\phi of the phase difference between two arms of an interferometer. For an
optimal measurement [B. C. Sanders and G. J. Milburn, Phys. Rev. Lett. 75, 2944
(1995)], it yields a variance (\Delta \phi)^2 \simeq \pi^2/N^2, compared to
O(N^{-1}) or O(N^{-1/2}) for states considered by previous authors. Such a
measurement cannot be realized by counting photons in the interferometer
outputs. However, we introduce an adaptive measurement scheme that can be thus
realized, and show that it yields a variance in \phi very close to that from an
optimal measurement.Comment: 4 pages, 4 figures, journal versio
Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information
A rigorous lower bound is obtained for the average resolution of any estimate
of a shift parameter, such as an optical phase shift or a spatial translation.
The bound has the asymptotic form k_I/ where G is the generator of the
shift (with an arbitrary discrete or continuous spectrum), and hence
establishes a universally applicable bound of the same form as the usual
Heisenberg limit. The scaling constant k_I depends on prior information about
the shift parameter. For example, in phase sensing regimes, where the phase
shift is confined to some small interval of length L, the relative resolution
\delta\hat{\Phi}/L has the strict lower bound (2\pi e^3)^{-1/2}/,
where m is the number of probes, each with generator G_1, and entangling joint
measurements are permitted. Generalisations using other resource measures and
including noise are briefly discussed. The results rely on the derivation of
general entropic uncertainty relations for continuous observables, which are of
interest in their own right.Comment: v2:new bound added for 'ignorance respecting estimates', some
clarification
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