Quantum metrology aims to harness the power of quantum mechanics to make ultra-precise measurements. A crucial advantage of quantum metrology is that it provides high precision with a significantly lower particle flux. This is an important requirement for many applications such as in biological sensing , where disturbing the system can damage the sample, or in gravitational wave detection , where the lasers in the interferometer interact with the mirrors enough to degrade the measurement . It is known that an interferometer that utilizes a stream of independent particles is capable of measurement precision at the shot noise limit (SNL) 1=pn where n is the total number of particles used in the probe state. However, by making use of quantum mechanical properties this can be improved to the “Heisenberg limit" 1=n, for example by using maximally entangled NOON states . The problem with such an approach is that quantum states are notoriously fragile to particle losses, which typically collapse a state and destroys the phase information. A number of clever schemes have been devised with some robustness to loss which still capture sub-classical precision, but for realistic losses likely to be experienced in an experiment these schemes soon lose their advantage and are beaten by unentangled measurement schemes. A class of states that show the potential for a great improvement over the alternatives are the entangled coherent states (ECSs) [7, 8]. We show that these states allow substantial improvements over unentangled ‘classical’ states and highly-entangled NOON states for a wide range of loss values. We then look at the quantum mechanisms that lead to precise measurements. In optical interferometry multi-mode entanglement is often assumed to be the driving force behind quantum enhanced measurements. Recent work has shown this assumption to be false: single mode quantum states perform just as well as their multi-mode entangled counterparts. We go beyond this to show that when photon losses occur- an inevitability in any realistic system - multi-mode entanglement is actually detrimental to obtaining quantum enhanced measurements. We specifically apply this idea to a superposition of coherent states, demonstrating that these states show a robustness to loss that allows them to significantly outperform their competitors in realistic systems. A practically viable measurement scheme is then presented that allows measurements close to the theoretical bound, even with loss. These results promote a new way of approaching optical quantum metrology using single-mode states that we expect to have great implications for the future.
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