PROJECT TITLE: Recovering Information in Sloppy QUantum modEls (RISQUE)
Description
Over the last two decades, quantum estimation has offered a comprehensive framework to find the ultimate precision limits of quantum measurements, and to design novel quantum-enhanced sensing protocols. In the standard scenario, the quantities of interest are encoded as parameters in the evolution of the quantum state of a probe, which is then measured in order to obtain the values of those parameters with the lowest possible uncertainty.
It is often the case that the dynamics is dictated by a given combination of some parameters, while remaining largely unaffected by variations of individual parameters. Such models are known as ‘sloppy’ and appear to be remarkably frequent, if not ubiquitous, in multiparameter systems, regardless of their nature: there occur examples in system biology, radioactive decays, biochemistry. There is a mismatch between the predictive power of the model, which can nevertheless provide accurate accounts of the phenomena, and its descriptive power, being unable to assign accurate values to the parameters. This hampers the possibility of testing competing models for the description of the system.
The project RISQUE aims at investigating how to tackle problems in ‘sloppy’ quantum statistical models with the tools of quantum information.
Aims
We plan to investigate in detail the tradeoff between the sloppiness of the quantum statistical models and the efficiency of the corresponding sensing/estimation protocols. In particular, we will explore different designs in order to optimize the extraction of information, ranging from informationally complete measurements to binary detection schemes. Implementation, in terms of proof-of-principle experiments, will be performed using photonic platforms involving discrete and continuous variables.
We will also use different types of quantum control techniques to directly interfere with the imprinting stage of the estimation problem. A first attempt will be inspired by quantum information scrambling: the underlying idea is that by properly designing sequences of control pulses, one can induce dispersion of the information associated with the sloppy parameters, hence allowing one to recognize their individual action on the probe. A second possibility to ‘open the box’ consists in breaking its evolution by acting on the system with a measurement.
Expected Results
- Benchmarking strategies to reduce sloppiness against the ultimate quantum metrological limits.
- Applying quantum information scrambling to the diagnostics of optical communication links, in which many local perturbations (say, delays, phases, or losses) are distributed along the line.
- Studying of spatial distribution of field forces and/or temperature gradients.
- Assessing the relevance of weak measurements for sloppy models, and to what extent we can use their information-disturbance trade off to our advantage.
State of the art
The main goal of quantum metrology is to efficiently plan different types of experiments by minimizing the invested effort to overcome noisy fluctuations, such as those originating from fabrication errors and external fields, as well as and intrinsic limitations related to the formal structure of the quantum theory itself (e.g. the Heisenberg uncertainty principle). The potential applications of this approach span from probing delicate biological systems, to squeezing enhanced optical interferometry, gravitational wave detection, magnetometry, atomic clocks and atom based enhanced sensors.
Under rather general assumptions, the ultimate precision attainable in a quantum metrology procedure is ruled by the Quantum Cramér-Rao bound, an inequality that lower-bounds the attainable precision for the estimation of a parameter. In fact, it turns out that any estimation procedure aimed to recover the parameter via this optimal strategy dictated may become ineffective in the absence of prior information. These difficulties become even more dramatic in multi-parameter scenarios, in which one is asked to estimate more than a single unknown physical quantity at the same time. In many cases of physical interests, the impossibility of jointly measuring non-compatible quantum observables makes it theoretically impossible to reach the multi-parameter version of the Quantum Cramér-Rao threshold. An even more drastic limitation occurs when the various parameters partially or completely interfere in such a way that it is impossible for the experimenter to discriminate their individual effects. Examples of this behavior are well known in computation biology and chemistry where they are typically identified as sloppy models. Under these conditions the Quantum Cramér-Rao diverges, signaling that neither a careful choice of the state of the probing system, nor an optimization of the detection procedure can lead to a recovering of the parameters. The aim of RISQUE is to study these specific settings at the quantum level and to propose and experimentally implement strategies that could be used to restore the detection capability of the procedure.
Riferimento: PRIN 2022 – Codice progetto: 2022T25TR3 – CUP: F53D23001460006
Investimento totale del progetto: € 26.1898
Partner/proponente: Scuola Normale Superiore, Pisa (coordinatore); Università degli Studi di Milano Statale
Coordinatore dell’UdR Università degli Studi Roma Tre: Marco Barbieri
