54,909 research outputs found
Cram\'er-Rao bound for time-continuous measurements in linear Gaussian quantum systems
We describe a compact and reliable method to calculate the Fisher information
for the estimation of a dynamical parameter in a continuously measured linear
Gaussian quantum system. Unlike previous methods in the literature, which
involve the numerical integration of a stochastic master equation for the
corresponding density operator in a Hilbert space of infinite dimension, the
formulas here derived depends only on the evolution of first and second moments
of the quantum states, and thus can be easily evaluated without the need of any
approximation. We also present some basic but physically meaningful examples
where this result is exploited, calculating analytical and numerical bounds on
the estimation of the squeezing parameter for a quantum parametric amplifier,
and of a constant force acting on a mechanical oscillator in a standard
optomechanical scenario.Comment: 9 pages, 2 figure
Detecting Gaussian entanglement via extractable work
We show how the presence of entanglement in a bipartite Gaussian state can be
detected by the amount of work extracted by a continuos variable Szilard-like
device, where the bipartite state serves as the working medium of the engine.
We provide an expression for the work extracted in such a process and
specialize it to the case of Gaussian states. The extractable work provides a
sufficient condition to witness entanglement in generic two-mode states,
becoming also necessary for squeezed thermal states. We extend the protocol to
tripartite Gaussian states, and show that the full structure of inseparability
classes cannot be discriminated based on the extractable work. This suggests
that bipartite entanglement is the fundamental resource underpinning work
extraction.Comment: 12 pages, 8 figure
Metrology with Unknown Detectors
The best possible precision is one of the key figures in metrology, but this
is established by the exact response of the detection apparatus, which is often
unknown. There exist techniques for detector characterisation, that have been
introduced in the context of quantum technologies, but apply as well for
ordinary classical coherence; these techniques, though, rely on intense data
processing. Here we show that one can make use of the simpler approach of data
fitting patterns in order to obtain an estimate of the Cram\'er-Rao bound
allowed by an unknown detector, and present applications in polarimetry.
Further, we show how this formalism provide a useful calculation tool in an
estimation problem involving a continuous-variable quantum state, i.e. a
quantum harmonic oscillator
Non-equilibrium readiness and accuracy of Gaussian Quantum Thermometers
The dimensionality of a thermometer is key in the design of quantum
thermometry schemes. In general, the phenomenology that is typical of
finite-dimensional quantum thermometry does not apply to infinite dimensional
ones. We analyse the dynamical and metrological features of non-equilibrium
Gaussian Quantum Thermometers: on one hand, we highlight how quantum
entanglement can enhance the readiness of composite Gaussian thermometers; on
the other hand, we show that non-equilibrium conditions do not guarantee the
best sensitivities in temperature estimation, thus suggesting the reassessment
of the working principles of quantum thermometry
Monitoring dispersive samples with single photons: the role of frequency correlations
The physics that governs quantum monitoring may involve other degrees of
freedom than the ones initialised and controlled for probing. In this context
we address the simultaneous estimation of phase and dephasing characterizing a
dispersive medium, and we explore the role of frequency correlations within a
photon pair generated via parametric down-conversion, when used as a probe for
the medium. We derive the ultimate quantum limits on the estimation of the two
parameters, by calculating the corresponding quantum Cram\'er-Rao bound; we
then consider a feasible estimation scheme, based on the measurement of Stokes
operators, and address its absolute performances in terms of the correlation
parameters, and, more fundamentally, of the role played by correlations in the
simultaneous achievability of the quantum Cram\'er-Rao bounds for each of the
two parameters.Comment: to appear in Quantum Measurements and Quantum Metrolog
Electrification in granular gases leads to constrained fractal growth
The empirical observation of aggregation of dielectric particles under the
influence of electrostatic forces lies at the origin of the theory of
electricity. The growth of clusters formed of small grains underpins a range of
phenomena from the early stages of planetesimal formation to aerosols. However,
the collective effects of Coulomb forces on the nonequilibrium dynamics and
aggregation process in a granular gas -- a model representative of the above
physical processes -- have so far evaded theoretical scrutiny. Here, we
establish a hydrodynamic description of aggregating granular gases that
exchange charges upon collisions and interact via the long-ranged Coulomb
forces. We analytically derive the governing equations for the evolution of
granular temperature, charge variance, and number density for homogeneous and
quasi-monodisperse aggregation. We find that, once the aggregates are formed,
the system obeys a physical constraint of nearly constant dimensionless ratio
of characteristic electrostatic to kinetic energy . This
constraint on the collective evolution of charged clusters is confirmed both by
the theory and the detailed molecular dynamics simulations. The inhomogeneous
aggregation of monomers and clusters in their mutual electrostatic field
proceeds in a fractal manner. Our theoretical framework is extendable to more
precise charge exchange mechanism, a current focus of extensive
experimentation. Furthermore, it illustrates the collective role of long-ranged
interactions in dissipative gases and can lead to novel designing principles in
particulate systems
- …