21 research outputs found
Measuring non-linear functionals of quantum harmonic oscillator states
Using only linear interactions and a local parity measurement we show how
entanglement can be detected between two harmonic oscillators. The scheme
generalizes to measure both linear and non-linear functionals of an arbitrary
oscillator state. This leads to many applications including purity tests,
eigenvalue estimation, entropy and distance measures - all without the need for
non-linear interactions or complete state reconstruction. Remarkably,
experimental realization of the proposed scheme is already within the reach of
current technology with linear optics.Comment: 5 pages, 2 figures. Minor corrections and some new references adde
Retrodictive quantum state engineering
This thesis is concerned with retrodiction and measurement in quantum optics.
The latter of these two concepts is studied in particular form with a general
optical multiport device, consisting of an arbitrary array of beam-splitters
and phase-shifters. I show how such an apparatus generalizes the original
projection synthesis technique, introduced as an in principle technique to
measure the canonical phase distribution. Just as for the original projection
synthesis, it is found that such a generalised device can synthesize any
general projection onto a state in a finite dimensional Hilbert space. One of
the important findings of this thesis is that, unlike the original projection
synthesis technique, the general apparatus described here only requires a
classical, that is a coherent, reference field at the input of the device. Such
an apparatus lends itself much more readily to practical implementation and
would find applications in measurement and predictive state engineering.
If we relax the above condition to allow for just a single non-classical
reference field, we show that the apparatus is capable of producing a
single-shot measure of canonical phase. That is, the apparatus can project onto
any one of an arbitrarily large subset of phase eigenstates, with a probability
proportional to the overlap of the phase state and the input field. Unlike the
original projection synthesis proposal, this proposal requires a binomial
reference state as opposed to a reciprocal binomial state. We find that such a
reference state can be obtained, to an excellent approximation, from a suitably
squeezed state.
The analysis of these measurement apparatuses is performed in the less usual,
but completely rigorous, retrodictive formalism of quantum mechanics.Comment: Ph.D thesis. Submitted April 200
Retrodictive quantum optical state engineering
Although it has been known for some time that quantum mechanics can be
formulated in a way that treats prediction and retrodiction on an equal
footing, most attention in engineering quantum states has been devoted to
predictive states, that is, states associated with the a preparation event.
Retrodictive states, which are associated with a measurement event and
propagate backwards in time, are also useful, however. In this paper we show
how any retrodictive state of light that can be written to a good approximation
as a finite superposition of photon number states can be generated by an
optical multiport device. The composition of the state is adjusted by
controlling predictive coherent input states. We show how the probability of
successful state generation can be optimised by adjusting the multiport device
and also examine a versatile configuration that is useful for generating a
range of states.Comment: 14 pages, 1 figur
Time-reversal and super-resolving phase measurements
We demonstrate phase super-resolution in the absence of entangled states. The
key insight is to use the inherent time-reversal symmetry of quantum mechanics:
our theory shows that it is possible to \emph{measure}, as opposed to prepare,
entangled states. Our approach is robust, requiring only photons that exhibit
classical interference: we experimentally demonstrate high-visibility phase
super-resolution with three, four, and six photons using a standard laser and
photon counters. Our six-photon experiment demonstrates the best phase
super-resolution yet reported with high visibility and resolution.Comment: 4 pages, 3 figure
Fidelity for imperfect postselection
We describe a simple measure of fidelity for mixed state postselecting
devices. The measure is most appropriate for postselection where the task
performed by the output is only effected by a specific state.Comment: 8 Pages, 8 Figure
Single-shot measurement of quantum optical phase
Although the canonical phase of light, which is defined as the complement of
photon number, has been described theoretically by a variety of distinct
approaches, there have been no methods proposed for its measurement. Indeed
doubts have been expressed about whether or not it is measurable. Here we show
how it is possible, at least in principle, to perform a single-shot measurement
of canonical phase using beam splitters, mirrors, phase shifters and
photodetectors.Comment: This paper was published in PRL in 2002 but, at the time, was not
placed on the archive. It is included now to make accessing this paper easie
Sub-Rayleigh-diffraction-bound quantum imaging
The spatial resolution of an imaging apparatus is limited by the Rayleigh diffraction bound, a consequence of the imagerâs finite spatial extent. We show some N-photon strategies that permit resolution of details that are smaller than this bound, attaining either a 1ââN enhancement (standard quantum limit) or a 1âN enhancement (Heisenberg-like scaling) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, since classical light sources suffice. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.DARPA Quantum Sensors ProgramW. M. Keck Foundation Center for Extreme Quantum Information Theor
Demonstration of Controllable Temporal Distinguishability in a Three-Photon State
Multi-photon interference is at the heart of the recently proposed linear
optical quantum computing scheme and plays an essential role in many protocols
in quantum information. Indistinguishability is what leads to the effect of
quantum interference. Optical interferometers such as Michaelson interferometer
provide a measure for second-order coherence at one-photon level and
Hong-Ou-Mandel interferometer was widely employed to describe two-photon
entanglement and indistinguishability. However, there is not an effective way
for a system of more than two photons. Recently, a new interferometric scheme
was proposed to quantify the degree of multi-photon distinguishability. Here we
report an experiment to implement the scheme for three-photon case. We are able
to generate three photons with different degrees of temporal distinguishability
and demonstrate how to characterize them by the visibility of three-photon
interference. This method of quantitative description of multi-photon
indistinguishability will have practical implications in the implementation of
quantum information protocols
Measuring Measurement: Theory and Practice
Recent efforts have applied quantum tomography techniques to the calibration
and characterization of complex quantum detectors using minimal assumptions. In
this work we provide detail and insight concerning the formalism, the
experimental and theoretical challenges and the scope of these tomographical
tools. Our focus is on the detection of photons with avalanche photodiodes and
photon number resolving detectors and our approach is to fully characterize the
quantum operators describing these detectors with a minimal set of well
specified assumptions. The formalism is completely general and can be applied
to a wide range of detectorsComment: 22 pages, 27 figure
Quantum nature of laser light
All compositions of a mixed-state density operator are equivalent for the
prediction of the probabilities of future outcomes of measurements. For
retrodiction, however, this is not the case. The retrodictive formalism of
quantum mechanics provides a criterion for deciding that some compositions are
fictional. Fictional compositions do not contain preparation device operators,
that is operators corresponding to states that could have been prepared. We
apply this to Molmer's controversial conjecture that optical coherences in
laser light are a fiction and find agreement with his conjecture. We generalise
Molmer's derivation of the interference between two lasers to avoid the use of
any fictional states. We also examine another possible method for
discriminating between conerent states and photon number states in laser light
and find that it does not work, with the equivalence for prediction saved by
entanglement