4,169 research outputs found
Adaptive Quantum Measurements of a Continuously Varying Phase
We analyze the problem of quantum-limited estimation of a stochastically
varying phase of a continuous beam (rather than a pulse) of the electromagnetic
field. We consider both non-adaptive and adaptive measurements, and both dyne
detection (using a local oscillator) and interferometric detection. We take the
phase variation to be \dot\phi = \sqrt{\kappa}\xi(t), where \xi(t) is
\delta-correlated Gaussian noise. For a beam of power P, the important
dimensionless parameter is N=P/\hbar\omega\kappa, the number of photons per
coherence time. For the case of dyne detection, both continuous-wave (cw)
coherent beams and cw (broadband) squeezed beams are considered. For a coherent
beam a simple feedback scheme gives good results, with a phase variance \simeq
N^{-1/2}/2. This is \sqrt{2} times smaller than that achievable by nonadaptive
(heterodyne) detection. For a squeezed beam a more accurate feedback scheme
gives a variance scaling as N^{-2/3}, compared to N^{-1/2} for heterodyne
detection. For the case of interferometry only a coherent input into one port
is considered. The locally optimal feedback scheme is identified, and it is
shown to give a variance scaling as N^{-1/2}. It offers a significant
improvement over nonadaptive interferometry only for N of order unity.Comment: 11 pages, 6 figures, journal versio
Phase measurements at the theoretical limit
It is well known that the result of any phase measurement on an optical mode
made using linear optics has an introduced uncertainty in addition to the
intrinsic quantum phase uncertainty of the state of the mode. The best
previously published technique [H. M. Wiseman and R.B. Killip, Phys. Rev. A 57,
2169 (1998)] is an adaptive technique that introduces a phase variance that
scales as n^{-1.5}, where n is the mean photon number of the state. This is far
above the minimum intrinsic quantum phase variance of the state, which scales
as n^{-2}. It has been shown that a lower limit to the phase variance that is
introduced scales as ln(n)/n^2. Here we introduce an adaptive technique that
attains this theoretical lower limit.Comment: 9 pages, 5 figures, updated with better feedback schem
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
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
On quantum error-correction by classical feedback in discrete time
We consider the problem of correcting the errors incurred from sending
quantum information through a noisy quantum environment by using classical
information obtained from a measurement on the environment. For discrete time
Markovian evolutions, in the case of fixed measurement on the environment, we
give criteria for quantum information to be perfectly corrigible and
characterize the related feedback. Then we analyze the case when perfect
correction is not possible and, in the qubit case, we find optimal feedback
maximizing the channel fidelity.Comment: 11 pages, 1 figure, revtex
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
Stochastic Heisenberg limit: Optimal estimation of a fluctuating phase
The ultimate limits to estimating a fluctuating phase imposed on an optical
beam can be found using the recently derived continuous quantum Cramer-Rao
bound. For Gaussian stationary statistics, and a phase spectrum scaling
asymptotically as 1/omega^p with p>1, the minimum mean-square error in any
(single-time) phase estimate scales as N^{-2(p-1)/(p+1)}, where N is the photon
flux. This gives the usual Heisenberg limit for a constant phase (as the limit
p--> infinity) and provides a stochastic Heisenberg limit for fluctuating
phases. For p=2 (Brownian motion), this limit can be attained by phase
tracking.Comment: 5+4 pages, to appear in Physical Review Letter
Quantum measurement and the first law of thermodynamics: the energy cost of measurement is the work value of the acquired information
The energy cost of measurement is an interesting fundamental question, and
may have profound implications for quantum technologies. In the context of
Maxwell's demon, it is often stated that measurement has no minimum energy
cost, while information has a work value, even though these statements can
appear contradictory. However, as we elucidate, these statements do no refer to
the cost paid by the measuring device. Here we show that it is only when a
measuring device has access to a zero temperature reservoir - that is, never -
that the measurement requires no energy. All real measuring devices pay the
cost that a heat engine pays to obtain the work value of the information they
acquire.Comment: 4 pages, revtex4-1. v2: added a referenc
Nuclear mutations affecting mitochondrial structure and function in Chlamydomonas
Wild type cells of the green alga Chlamydomonas reinhardtii can grow in the in the dark by taking up and respiring exogenously supplied acetate. Obligate photoautotrophic (dark dier, dk) mutants of this alga have been selected which grow at near wild type rates in the light, but rapidly die when transferred to darkness because of defects in mitochondrial structure and function. In crosses of the dk mutants to wild type, the majority of the mutants are inherited in a mendelian fashion, although two have been isolated which are inherited in a clearly nonmendelian fashion. Nine mendelian dk mutants have been analyzed in detail, and belong to eight different complementation groups representing eight gene loci. These mutants have been tentatively grouped into three classes on the basis of the pleiotropic nature of their phenotypic defects. Mutants in Class I have gross alterations in the ultrastructure of their mitochondrial inner membranes together with deficiencies in cytochrome oxidase and antimycin/rotenone-sensitive NADH-cytochrome c reductase activities. Mutants in Class II have a variety of less severe alterations in mitochondrial ultrastructure and deficiencies in cytochrome oxidase activity. Mutants in Class III have normal or near normal mitochondrial ultrastructure and reduced cytochrome oxidase activity. Eight of the nine mutants show corresponding reductions in cyanide-sensitive respiration
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
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