539 research outputs found
Optimal phase measurements with pure Gaussian states
We analyze the Heisenberg limit on phase estimation for Gaussian states. In
the analysis, no reference to a phase operator is made. We prove that the
squeezed vacuum state is the most sensitive for a given average photon number.
We provide two adaptive local measurement schemes that attain the Heisenberg
limit asymptotically. One of them is described by a positive operator-valued
measure and its efficiency is exhaustively explored. We also study Gaussian
measurement schemes based on phase quadrature measurements. We show that
homodyne tomography of the appropriate quadrature attains the Heisenberg limit
for large samples. This proves that this limit can be attained with local
projective Von Neuman measurements.Comment: 9 pages. Revised version: two new sections added, revised
conclusions. Corrected prose. Corrected reference
Discrimination of Optical Coherent States using a Photon Number Resolving Detector
The discrimination of non-orthogonal quantum states with reduced or without
errors is a fundamental task in quantum measurement theory. In this work, we
investigate a quantum measurement strategy capable of discriminating two
coherent states probabilistically with significantly smaller error
probabilities than can be obtained using non-probabilistic state
discrimination. We find that appropriate postselection of the measurement data
of a photon number resolving detector can be used to discriminate two coherent
states with small error probability. We compare our new receiver to an optimal
intermediate measurement between minimum error discrimination and unambiguous
state discrimination.Comment: 5 pages, 4 figure
The Effect of the LISA Response Function on Observations of Monochromatic Sources
The Laser Interferometer Space Antenna (LISA) is expected to provide the
largest observational sample of binary systems of faint sub-solar mass compact
objects, in particular white-dwarfs, whose radiation is monochromatic over most
of the LISA observational window. Current astrophysical estimates suggest that
the instrument will be able to resolve about 10000 such systems, with a large
fraction of them at frequencies above 3 mHz, where the wavelength of
gravitational waves becomes comparable to or shorter than the LISA arm-length.
This affects the structure of the so-called LISA transfer function which cannot
be treated as constant in this frequency range: it introduces characteristic
phase and amplitude modulations that depend on the source location in the sky
and the emission frequency. Here we investigate the effect of the LISA transfer
function on detection and parameter estimation for monochromatic sources. For
signal detection we show that filters constructed by approximating the transfer
function as a constant (long wavelength approximation) introduce a negligible
loss of signal-to-noise ratio -- the fitting factor always exceeds 0.97 -- for
f below 10mHz, therefore in a frequency range where one would actually expect
the approximation to fail. For parameter estimation, we conclude that in the
range 3mHz to 30mHz the errors associated with parameter measurements differ
from about 5% up to a factor of 10 (depending on the actual source parameters
and emission frequency) with respect to those computed using the long
wavelength approximation.Comment: replacement version with typos correcte
Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
We examine whether metrological resolution beyond coherent states is a
nonclassical effect. We show that this is true for linear detection schemes but
false for nonlinear schemes, and propose a very simple experimental setup to
test it. We find a nonclassicality criterion derived from quantum Fisher
information.Comment: 4 pages, 1 figur
PPM demodulation: On approaching fundamental limits of optical communications
We consider the problem of demodulating M-ary optical PPM (pulse-position
modulation) waveforms, and propose a structured receiver whose mean probability
of symbol error is smaller than all known receivers, and approaches the quantum
limit. The receiver uses photodetection coupled with optimized phase-coherent
optical feedback control and a phase-sensitive parametric amplifier. We present
a general framework of optical receivers known as the conditional pulse nulling
receiver, and present new results on ultimate limits and achievable regions of
spectral versus photon efficiency tradeoffs for the single-spatial-mode
pure-loss optical communication channel.Comment: 5 pages, 6 figures, IEEE ISIT, Austin, TX (2010
Ziv-Zakai Error Bounds for Quantum Parameter Estimation
I propose quantum versions of the Ziv-Zakai bounds as alternatives to the
widely used quantum Cram\'er-Rao bounds for quantum parameter estimation. From
a simple form of the proposed bounds, I derive both a "Heisenberg" error limit
that scales with the average energy and a limit similar to the quantum
Cram\'er-Rao bound that scales with the energy variance. These results are
further illustrated by applying the bound to a few examples of optical phase
estimation, which show that a quantum Ziv-Zakai bound can be much higher and
thus tighter than a quantum Cram\'er-Rao bound for states with highly
non-Gaussian photon-number statistics in certain regimes and also stay close to
the latter where the latter is expected to be tight.Comment: v1: preliminary result, 3 pages; v2: major update, 4 pages +
supplementary calculations, v3: another major update, added proof of
"Heisenberg" limit, v4: accepted by PR
Optimal estimation of quantum observables
We consider the problem of estimating the ensemble average of an observable
on an ensemble of equally prepared identical quantum systems. We show that,
among all kinds of measurements performed jointly on the copies, the optimal
unbiased estimation is achieved by the usual procedure that consists in
performing independent measurements of the observable on each system and
averaging the measurement outcomes.Comment: Submitted to J. Math Phy
Universal measurement apparatus controlled by quantum software
We propose a quantum device that can approximate any projective measurement
on a qubit. The desired measurement basis is selected by the quantum state of a
"program register". The device is optimized with respect to maximal average
fidelity (assuming uniform distribution of measurement bases). An interesting
result is that if one uses two qubits in the same state as a program the
average fidelity is higher than if he/she takes the second program qubit in the
orthogonal state (with respect to the first one). The average information
obtainable by the proposed measurements is also calculated and it is shown that
it can get different values even if the average fidelity stays constant.
Possible experimental realization of the simplest proposed device is presented.Comment: 4 pages, 2 figures, reference adde
Extremal covariant measurements
We characterize the extremal points of the convex set of quantum measurements
that are covariant under a finite-dimensional projective representation of a
compact group, with action of the group on the measurement probability space
which is generally non-transitive. In this case the POVM density is made of
multiple orbits of positive operators, and, in the case of extremal
measurements, we provide a bound for the number of orbits and for the rank of
POVM elements. Two relevant applications are considered, concerning state
discrimination with mutually unbiased bases and the maximization of the mutual
information.Comment: 11 pages, no figure
Sub Shot-Noise Phase Sensitivity with a Bose-Einstein Condensate Mach-Zehnder Interferometer
Bose Einstein Condensates, with their coherence properties, have attracted
wide interest for their possible application to ultra precise interferometry
and ultra weak force sensors. Since condensates, unlike photons, are
interacting, they may permit the realization of specific quantum states needed
as input of an interferometer to approach the Heisenberg limit, the supposed
lower bound to precision phase measurements. To this end, we study the
sensitivity to external weak perturbations of a representative matter-wave
Mach-Zehnder interferometer whose input are two Bose-Einstein condensates
created by splitting a single condensate in two parts. The interferometric
phase sensitivity depends on the specific quantum state created with the two
condensates, and, therefore, on the time scale of the splitting process. We
identify three different regimes, characterized by a phase sensitivity scaling with the total number of condensate particles as i) the
standard quantum limit , ii) the sub shot-noise
and the iii) the Heisenberg limit . However, in a realistic dynamical BEC splitting, the 1/N limit
requires a long adiabaticity time scale, which is hardly reachable
experimentally. On the other hand, the sub shot-noise sensitivity can be reached in a realistic experimental setting. We
also show that the scaling is a rigorous upper bound in the limit
, while keeping constant all different parameters of the bosonic
Mach-Zehnder interferometer.Comment: 4 figure
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