626 research outputs found
Fisher information and asymptotic normality in system identification for quantum Markov chains
This paper deals with the problem of estimating the coupling constant
of a mixing quantum Markov chain. For a repeated measurement on the
chain's output we show that the outcomes' time average has an asymptotically
normal (Gaussian) distribution, and we give the explicit expressions of its
mean and variance. In particular we obtain a simple estimator of whose
classical Fisher information can be optimized over different choices of
measured observables. We then show that the quantum state of the output
together with the system, is itself asymptotically Gaussian and compute its
quantum Fisher information which sets an absolute bound to the estimation
error. The classical and quantum Fisher informations are compared in a simple
example. In the vicinity of we find that the quantum Fisher
information has a quadratic rather than linear scaling in output size, and
asymptotically the Fisher information is localised in the system, while the
output is independent of the parameter.Comment: 10 pages, 2 figures. final versio
Squeezed vacuum as a universal quantum probe
We address local quantum estimation of bilinear Hamiltonians probed by
Gaussian states. We evaluate the relevant quantum Fisher information (QFI) and
derive the ultimate bound on precision. Upon maximizing the QFI we found that
single- and two-mode squeezed vacuum represent an optimal and universal class
of probe states, achieving the so-called Heisenberg limit to precision in terms
of the overall energy of the probe. We explicitly obtain the optimal observable
based on the symmetric logarithmic derivative and also found that homodyne
detection assisted by Bayesian analysis may achieve estimation of squeezing
with near-optimal sensitivity in any working regime. Besides, by comparison of
our results with those coming from global optimization of the measurement we
found that Gaussian states are effective resources, which allow to achieve the
ultimate bound on precision imposed by quantum mechanics using measurement
schemes feasible with current technology.Comment: revised version, 2 figure
Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras
A geometrical formulation of estimation theory for finite-dimensional
-algebras is presented. This formulation allows to deal with the
classical and quantum case in a single, unifying mathematical framework. The
derivation of the Cramer-Rao and Helstrom bounds for parametric statistical
models with discrete and finite outcome spaces is presented.Comment: 33 pages. Minor improvements. References added. Comments are welcome
Quantum reading of quantum information
We extend the notion of quantum reading to the case where the information to be retrieved, which is encoded into a set of quantum channels, is of quantum nature. We use two-qubit unitaries describing the system-environment interaction, with the initial environment state determining the system's input-output channel and hence the encoded information. The performance of the most relevant two-qubit unitaries is determined with two different approaches: (i) one-shot quantum capacity of the channel arising between environment and system's output; (ii) estimation of parameters characterizing the initial quantum state of the environment. The obtained results are mostly in (qualitative) agreement, with some distinguishing features that include the CNOT unitary
Quantum reading of quantum information
We extend the notion of quantum reading to the case where the information to
be retrieved, which is encoded into a set of quantum channels, is of quantum
nature. We use two qubit unitaries describing the system environment
interaction, with the initial environment state determining the system's input
output channel and hence the encoded information. The performance of the most
relevant two-qubit unitaries is determined with two different approaches: i)
one-shot quantum capacity of the channel arising between environment and
system's output; ii) estimation of parameters characterizing the initial
quantum state of the environment. The obtained results are mostly in
(qualitative) agreement, with some distinguishing features that include the
CNOT unitary.Comment: Relations/differences with respect to previous works are better
explained, and new references are adde
On the existence of unbiased resilient estimators in discrete quantum systems
Cram\'er-Rao constitutes a crucial lower bound for the mean squared error of
an estimator in frequentist parameter estimation, albeit paradoxically
demanding highly accurate prior knowledge of the parameter to be estimated.
Indeed, this information is needed to construct the optimal unbiased estimator,
which is highly dependent on the parameter. Conversely, Bhattacharyya bounds
result in a more resilient estimation about prior accuracy by imposing
additional constraints on the estimator. Initially, we conduct a quantitative
comparison of the performance between Cram\'er-Rao and Bhattacharyya bounds
when faced with less-than-ideal prior knowledge of the parameter. Furthermore,
we demonstrate that the order classical and quantum Bhattacharyya
bounds cannot be computed -- given the absence of estimators satisfying the
constraints -- under specific conditions tied to the dimension of the
discrete system. Intriguingly, for a system with the same dimension , the
maximum non-trivial order is in the classical case, while in the
quantum realm, it extends to . Consequently, for a given system
dimension, one can construct estimators in quantum systems that exhibit
increased robustness to prior ignorance.Comment: typos corrected and we extended some explanation
High posterior density ellipsoids of quantum states
Regions of quantum states generalize the classical notion of error bars. High
posterior density (HPD) credible regions are the most powerful of region
estimators. However, they are intractably hard to construct in general. This
paper reports on a numerical approximation to HPD regions for the purpose of
testing a much more computationally and conceptually convenient class of
regions: posterior covariance ellipsoids (PCEs). The PCEs are defined via the
covariance matrix of the posterior probability distribution of states. Here it
is shown that PCEs are near optimal for the example of Pauli measurements on
multiple qubits. Moreover, the algorithm is capable of producing accurate PCE
regions even when there is uncertainty in the model.Comment: TL;DR version: computationally feasible region estimator
Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure
The most direct probe of non-Gaussian initial conditions has come from
bispectrum measurements of temperature fluctuations in the Cosmic Microwave
Background and of the matter and galaxy distribution at large scales. Such
bispectrum estimators are expected to continue to provide the best constraints
on the non-Gaussian parameters in future observations. We review and compare
the theoretical and observational problems, current results and future
prospects for the detection of a non-vanishing primordial component in the
bispectrum of the Cosmic Microwave Background and large-scale structure, and
the relation to specific predictions from different inflationary models.Comment: 82 pages, 23 figures; Invited Review for the special issue "Testing
the Gaussianity and Statistical Isotropy of the Universe" for Advances in
Astronom
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