Multi-mode interferometers for bosons in Gaussian states are important systems for quantum metrology with precision beyond the standard quantum limit and for bosonic quantum computing. However, there is a lack of theoretical foundation for generic
N-mode Gaussian interferometry. In this work, we study quantum metrology and quantum control in multi-mode bosonic systems with quadratic Hamiltonians, exploiting the fundamental Sp
(2N,R) symmetry of such interferometers. We show that the optimal quantum control to maximize sensitivity requires aligning squeezing and displacement in the same direction. We propose Sp
(2N,R) echo, a multi-mode generalization of the SU
(1,1) interferometry, to achieve the sensitivity of phase estimation set by the quantum Fisher information. In addition, we introduce a geometrical means for reversing many-body dynamics with Sp
(2N,R) dynamical symmetry, such as dynamics of the bosonic Kitaev chain. Our schemes are readily realizable in optical, atomic, and mechanical platforms.
Optical and optomechanical systems are exploited for quantum technologies to perform highly precise measurements for fundamental physics as well as biological and engineering tasks. Theoretical studies using tools from statistics and quantum information can greatly aid studies of the sensing capabilities of quantum systems and experimental designs. These allow us to quantify the amount of information about a parameter encoded in a quantum state itself and examine how that can be extracted through measurements. In this thesis we show how mechanical squeezing and measurements beyond position can be utilised to improve the precision of wavepacket expansion measurements which can test collapse models of quantum mechanics. Particularly, that squeezing can compensate for the free-fall time which is often the most significant limiting factor in such experiments, and measurements of other quadratures can offer increased precision. We demonstrate that the use of additional optical fields to measure the displacement of a free mass in a radiation-pressure limited interferometer cannot surpass the ultimate precision of the single-mode interferometer. This work applies to the likes of laser-interferometric gravitational wave detectors. Finally, we venture into multi-parameter estimation: we calculate bounds for multi-mode Gaussian states used to estimate many phase shifts and optimise over the input states. In contrast to the—far less experimentally feasible—multi-mode generalisations of N00N states we see no significant improvement when using multi-mode Gaussian states for the task. Given their comparable performance in single-phase estimation this is a new limitation of Gaussian states appearing only at the multi-parameter level.
Quantum correlations can be harnessed to improve the precision in parameter estimation beyond classical capabilities. Under a standard interferometric or rotation protocol, it is well established that the optimal single-mode Gaussian state is a standard squeezed vacuum, which enables Heisenberg limited precision. In this work, we investigate the potential metrological advantage of two distinct families involving high-order squeezing, namely, mth-phase and multisqueezed states. Our results show that these non-Gaussian states can grant a significant metrological advantage with respect to the optimal squeezed vacuum under equivalent conditions, i.e. at equal occupations. Their advantage holds both at low and large occupations, but its behavior critically depends on the chosen family of high-order squeezing. While higher squeezing orders enhance the advantage, this comes at the cost of higher-order observables in the measurement for full metrological performance. Finally, we study their robustness to standard decoherence channels, i.e. pure dephasing and zero-temperature damping. Employing standard squeezing as reference state, our results indicate a reasonable robustness against damping up to a certain noise strength, while their metrological advantage becomes fragile under pure dephasing. Our work shows the potential enhancement in quantum metrology beyond Gaussian states, carefully detailing the main challenges and limitations.
The ubiquitous presence of shot noise sets a fundamental limit to the measurement precision in classical metrology. Recent advances in quantum devices and novel quantum algorithms utilizing interference effects are opening new routes for overcoming the detrimental noise tyranny. However, further progress is limited by the restricted capability of existing algorithms to account for the decoherence pervading experimental implementations. Here, adopting a systematic approach to the evaluation of effectiveness of metrological procedures, we devise the Linear Ascending Metrological Algorithm (LAMA), which offers a remarkable increase in precision in the demanding situation where a decohering quantum system is used to measure a continuously distributed variable. We introduce our protocol in the context of magnetic field measurements, assuming superconducting transmon devices as sensors operated in a qudit mode. Our findings demonstrate a quantum-metrological procedure capable of mitigating detrimental dephasing and relaxation effects.