12 research outputs found
Frequentist and Bayesian Quantum Phase Estimation
Frequentist and Bayesian phase estimation strategies lead to conceptually
different results on the state of knowledge about the true value of the phase
shift. We compare the two frameworks and their sensitivity bounds to the
estimation of an interferometric phase shift limited by quantum noise,
considering both the cases of a fixed and a fluctuating parameter. We point out
that frequentist precision bounds, such as the Cram\`er-Rao bound, for
instance, do not apply to Bayesian strategies and vice-versa. Similarly, bounds
for fluctuating parameters make no statement about the estimation of a fixed
parameter.Comment: 4 figure
RLD Fisher information bound for multiparameter estimation of quantum channels
One of the fundamental tasks in quantum metrology is to estimate multiple parameters embedded in a noisy process, i.e. a quantum channel. In this paper, we study fundamental limits to quantum channel estimation via the concept of amortization and the right logarithmic derivative (RLD) Fisher information value. Our key technical result is the proof of a chain-rule inequality for the RLD Fisher information value, which implies that amortization, i.e. access to a catalyst state family, does not increase the RLD Fisher information value of quantum channels. This technical result leads to a fundamental and efficiently computable limitation for multiparameter channel estimation in the sequential setting, in terms of the RLD Fisher information value. As a consequence, we conclude that if the RLD Fisher information value is finite, then Heisenberg scaling is unattainable in the multiparameter setting
Quantum Scale Estimation
Quantum scale estimation, as introduced and explored here, establishes the
most precise framework for the estimation of scale parameters which is allowed
by the laws of quantum mechanics. This addresses an important gap in quantum
metrology, since current practice focuses almost exclusively on the estimation
of phase and location parameters. For given prior probability and quantum
state, and using Bayesian principles, a rule to construct the optimal
probability-operator measurement is provided. Furthermore, the corresponding
minimum mean logarithmic error is identified. This is then generalised as to
accommodate the simultaneous estimation of multiple scale parameters, and a
procedure to classify practical measurements into optimal, almost-optimal or
sub-optimal is highlighted. As an application, the framework of scale-invariant
global thermometry is revisited and generalised. On a more conceptual note, the
optimal strategy is employed to construct an observable for scale parameters,
an approach which may serve as a template for a more systematic search of
quantum observables. Quantum scale estimation thus opens a new line of enquire
- the precise measurement of scale parameters such as temperatures and rates -
within the quantum information sciences.Comment: 15 pages, 1 table. More explicit definition of scale parameter.
Manuscript updated accordingly, but same results. Multi-shot subsection
removed for simplicity. Discussion of quantum thermometry protocols
considerably expande
Deep reinforcement learning for quantum multiparameter estimation
Estimation of physical quantities is at the core of most scientific research, and the use of quantum devices promises to enhance its performances. In real scenarios, it is fundamental to consider that resources are limited, and Bayesian adaptive estimation represents a powerful approach to efficiently allocate, during the estimation process, all the available resources. However, this framework relies on the precise knowledge of the system model, retrieved with a fine calibration, with results that are often computationally and experimentally demanding. We introduce a model-free and deep-learning-based approach to efficiently implement realistic Bayesian quantum metrology tasks accomplishing all the relevant challenges, without relying on any a priori knowledge of the system. To overcome this need, a neural network is trained directly on experimental data to learn the multiparameter Bayesian update. Then the system is set at its optimal working point through feedback provided by a reinforcement learning algorithm trained to reconstruct and enhance experiment heuristics of the investigated quantum sensor. Notably, we prove experimentally the achievement of higher estimation performances than standard methods, demonstrating the strength of the combination of these two black-box algorithms on an integrated photonic circuit. Our work represents an important step toward fully artificial intelligence-based quantum metrology
Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations
Using quantum systems as sensors or probes has been shown to greatly improve
the precision of parameter estimation by exploiting unique quantum features
such as entanglement. A major task in quantum sensing is to design the optimal
protocol, i.e., the most precise one. It has been solved for some specific
instances of the problem, but in general even numerical methods are not known.
Here, we focus on the single-shot Bayesian setting, where the goal is to find
the optimal initial state of the probe (which can be entangled with an
auxiliary system), the optimal measurement, and the optimal estimator function.
We leverage the formalism of higher-order operations to develop a method based
on semidefinite programming that finds a protocol that is close to the optimal
one with arbitrary precision. Crucially, our method is not restricted to any
specific quantum evolution, cost function or prior distribution, and thus can
be applied to any estimation problem. Moreover, it can be applied to both
single or multiparameter estimation tasks. We demonstrate our method with three
examples, consisting of unitary phase estimation, thermometry in a bosonic
bath, and multiparameter estimation of an SU(2) transformation. Exploiting our
methods, we extend several results from the literature. For example, in the
thermometry case, we find the optimal protocol at any finite time and quantify
the usefulness of entanglement. Additionally, we show that when the cost
function is the mean squared error, projective measurements are optimal for
estimation.Comment: 13 + 8 pages, 6 figure
Quantum scale estimation
This is the author accepted manuscript. The final version is available from IOP Publishing via the DOI in this recordQuantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology, since current practice focuses almost exclusively on the estimation of phase and location parameters. For given prior probability and quantum state, and using Bayesian principles, a rule to construct the optimal probability-operator measurement is provided. Furthermore, the corresponding minimum mean logarithmic error is identified. This is then generalised as to accommodate the simultaneous estimation of multiple scale parameters, and a procedure to classify practical measurements into optimal, almost-optimal or sub-optimal is highlighted. As a means of illustration, the new framework is exploited to generalise scale-invariant global thermometry, as well as to address the estimation of the lifetime of an atomic state. On a more conceptual note, the optimal strategy is employed to construct an observable for scale parameters, an approach which may serve as a template for a more systematic search of quantum observables. Quantum scale estimation thus opens a new line of enquire - the precise measurement of scale parameters such as temperatures and rates - within the quantum information sciences.Engineering and Physical Sciences Research CouncilEngineering and Physical Sciences Research Counci