One of the first goals of this fellowship was to develop theoretical tools for quantum sensing, specifically for the problems
of discrimination and estimation of bosonic quantum channels. In this regard, I have contributed to review and further develop the theory
of channel simulation, which allows one to simplify the most general adaptive protocols of quantum hypothesis testing, quantum metrology
and quantum communication. This approach has led to very simple results, where the ultimate performances achievable for these tasks
can be computed over the so-called Choi states of the channels. Besides this exploration, I also analyzed the role of quantum discord
(i.e. quantum correlations beyond entanglement) in certain types of discrimination problems, and contributed to further advance the
fundamental protocol of quantum illumination, showing that the use of maximal entanglement is not strictly necessary to achieve
quantum advantage over classical strategies.
Besides this purely theoretical study, the most important goal of the fellowship was to demonstrate that quantum sources of light, combined with
suitable quantum measurements, could remarkably increase the current performances in the probing and scanning of fragile photo-degradable materials,
over which we can only irradiate a relatively-small number of photons. This goal has been demonstrated in a number of publications.
In a work called “Symmetric and asymmetric discrimination of bosonic loss: Toy applications to biological samples and photo-degradable materials”
[Phys. Rev. A 98, 053836 (2018)], I investigated the quantum discrimination of bosonic loss in the settings of symmetric and asymmetric hypothesis testing.
For both approaches, I found that an entangled resource is able to outperform any classical strategy based on coherent-state transmitters in the regime of
low photon numbers. In the symmetric case, I then considered the low energy detection of bacterial growth in culture media. Assuming an exponential growth law
for the bacterial concentration and the Beer-Lambert law for the optical transmissivity of the sample, I found that the use of entanglement allows
one to achieve a much faster detection of growth with respect to the use of coherent states. This performance was also studied by assuming an exponential
photo-degradable model, where the concentration is reduced by increasing the number of photons irradiated over the sample.
In the paper "Detecting and tracking bacteria with quantum light" [arXiv:2006.13250] I have further demonstrated that quantum sources of light
can successfully improve the current classical measurements that are performed on biological systems. I was able to show the superiority (and the limits)
of quantum resources for two basic tasks: the early detection of bacterial growth and the early discrimination between bacteria species
(such as E. Coli and Salmonella). Quantum advantage in detecting and identifying bacteria was shown with respect to a
realistic benchmark given by the actual performance of a state-of-the-art classical spectro-photometer.
According to my calculations, detection/identification of bacteria via quantum light could lead to a remarkable one-hour advantage
with respect to the classical setup, which may represent a non-trivial critical advantage in some operational scenarios.
In another work called “Thermal quantum metrology in memoryless and correlated environments” [Quantum Sci. Technol. 4, 015008 (2019)], I have designed an
optimal yet practical model of quantum spectro-photometer. In bosonic quantum metrology, the estimate of a loss parameter is typically performed by means
of pure states, such as coherent, squeezed or entangled states, while mixed thermal probes are discarded for their inferior performance.
In this work I instead showed that thermal sources with suitable correlations can be engineered in such a way to approach, or even surpass, the error scaling of
coherent states in the presence of general Gaussian decoherence. These findings pave the way for practical and optimal quantum metrology with thermal sources
in optical instruments, most importantly photometers, or at different wavelengths (e.g. far infrared, microwave or X-ray) where the generation of quantum features,
such as coherence, squeezing or entanglement, may be extremely challenging.
In conclusion, the following results were achieved:
1. Development of new mathematical tools for quantum sensing (and other areas).
2. Proof that quantum sources can improve detection/identification of bacteria or other photo-degradable material.
3. Proof that practical quantum sources and measurements can achieve a quantum advantage.
