### Abstract

The aim of this thesis is developing interferometric schemes which are scalableand can be implemented with current quantum optical technologies and yet

achieve quantum-enhanced metrological sensitivity. The fundamental precision

limit in classical interferometric schemes is the so-called standard quantum

limit. Harnessing distinctively quantum-mechanical features such as entanglement, quantum technologies have the potential to take us beyond what

is fundamentally impossible in a classical setting. Unfortunately, while it is

well known this is possible in theory, current optical technology can only produce

quantum resources which would not produce any appreciable quantum

advantage over classical methods.

The work presented in this thesis shows how squeezed states of light can

be used to overcome some of the most pressing technological limitations in

quantum metrology and can be used as a basis for an experimental demonstration of a quantum advantage in sensitivity with a significantly high mean photon number. The use of squeezed states allows us to forego the production of Fock states and difficult post-selection techniques for the creation of NOON states. It foregoes the reliance on entanglement to use as quantum

resource, except perhaps for the one that can be generated simply by running

photons through a linear optical network. Squeezed states also offer the technological advantage of foregoing number-resolving detectors in favour of more accessible on-off photodetectors.

A novel scheme for the estimation of a linear combination of phase shifts

with arbitrary non-negative weights is proposed which achieves the Heisenberg

limit. An intuitive graphical interpretation of the 2-mode scenario is found.

It turns out a Mach-Zehnder configuration can actually estimate either the

sum of the phase shifts associated to the two arms of the optical network–

provided the relative phase of the squeezers is known– with Heisenberg-limited

sensitivity, or the difference of the same phases at the standard quantum

limit. By introducing photon losses it is proven that the estimation protocol

in both cases is robust to detector inefficiencies. The interaction between

photon losses at the optical network level and at the detection level reveals

an unexpected dithering effect which can provide an advantage in the highlosses

regime.

Date of Award | 12 Mar 2023 |
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Original language | English |

Supervisor | Vincenzo Tamma (Supervisor) & Andrew Lundgren (Supervisor) |