6,317 research outputs found
Optical coherence and teleportation: Why a laser is a clock, not a quantum channel
It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. {\bf 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'. Van Enk, and Fuchs [Phys. Rev. Lett, {\bf 88}, 027902
(2002)], while arguing against Rudolph and Sanders, also accept that an
`absolute phase' is achievable, even if it has not been achieved yet. I will
argue to the contrary that `true coherence' or `absolute phase' is always
illusory, as the concept of absolute time on a scale beyond direct human
experience is meaningless. All we can ever do is to use an agreed time
standard. In this context, a laser beam is fundamentally as good a `clock' as
any other. I explain in detail why this claim is true, and defend my argument
against various objections. In the process I discuss super-selection rules,
quantum channels, and the ultimate limits to the performance of a laser as a
clock. For this last topic I use some earlier work by myself [Phys. Rev. A {\bf
60}, 4083 (1999)] and Berry and myself [Phys. Rev. A {\bf 65}, 043803 (2002)]
to show that a Heisenberg-limited laser with a mean photon number can
synchronize independent clocks each with a mean-square error of
radians.Comment: 14 pages, no figures, some equations this time. For proceedings of
SPIE conference "Fluctuations and Noise 2003
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
Selective linear or quadratic optomechanical coupling via measurement
The ability to engineer both linear and non-linear coupling with a mechanical
resonator is an important goal for the preparation and investigation of
macroscopic mechanical quantum behavior. In this work, a measurement based
scheme is presented where linear or square mechanical displacement coupling can
be achieved using the optomechanical interaction linearly proportional to the
mechanical position. The resulting square displacement measurement strength is
compared to that attainable in the dispersive case using the direct interaction
to the mechanical displacement squared. An experimental protocol and parameter
set are discussed for the generation and observation of non-Gaussian states of
motion of the mechanical element.Comment: 7 pages, 2 figures, (accepted in Physical Review X
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
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
Maximum information gain in weak or continuous measurements of qudits: complementarity is not enough
To maximize average information gain for a classical measurement, all
outcomes of an observation must be equally likely. The condition of equally
likely outcomes may be enforced in quantum theory by ensuring that one's state
is maximally different, or complementary, to the measured observable.
This requires the ability to perform unitary operations on the state,
conditioned on the results of prior measurements. We consider the case of
measurement of a component of angular momentum for a qudit (a -dimensional
system, with ). For weak or continuous-in-time (i.e. repeated weak)
measurements, we show that the complementarity condition ensures an average
improvement, in the rate of purification, of only 2. However, we show that by
choosing the optimal control protocol of this type, one can attain the best
possible scaling, , for the average improvement. For this protocol
the acquisition of information is nearly deterministic. Finally we contrast
these results with those for complementarity-based protocols in a register of
qbits.Comment: 21 pages, 21 figures. V2 published versio
Modal dynamics for positive operator measures
The modal interpretation of quantum mechanics allows one to keep the standard
classical definition of realism intact. That is, variables have a definite
status for all time and a measurement only tells us which value it had.
However, at present modal dynamics are only applicable to situations that are
described in the orthodox theory by projective measures. In this paper we
extend modal dynamics to include positive operator measures (POMs). That is,
for example, rather than using a complete set of orthogonal projectors, we can
use an overcomplete set of nonorthogonal projectors. We derive the conditions
under which Bell's stochastic modal dynamics for projective measures reduce to
deterministic dynamics, showing (incidentally) that Brown and Hiley's
generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus
derived. We then show how {\em deterministic} dynamics for positive operators
can also be derived. As a simple case, we consider a Harmonic oscillator, and
the overcomplete set of coherent state projectors (i.e. the Husimi POM). We
show that the modal dynamics for this POM in the classical limit correspond to
the classical dynamics, even for the nonclassical number state . This
is in contrast to the Bohmian dynamics, which for energy eigenstates, the
dynamics are always non-classical.Comment: 14 page
- …