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Adaptive Measurements In Quantum Metrology And State Discrimination


One of the strengths of quantum information science is that it provides a unified framework for discussing a range of quantum-enhanced technologies. Thus, ideas for using quantum resources to enhance information processing or communications can also be used to enhance measurement precision. One of the most interesting parallel areas is that of quantum control, where measurement and feedback techniques applied to quantum systems can be used to simplify protocols by reducing the required resources, or to make them more robust in the presence of noise.

I will discuss the experimental demonstration of two applications that benefit from the combination of quantum information insights and adaptive measurement, a technique from quantum control. The first application is quantum-enhanced precision measurement. Generally, estimation of a completely unknown phase has a sensitivity governed by the shot noise limit, because of the fact that resources are used independently. Using complex entangled states, such as the so-called NOON state, can theoretically improve the scaling of the phase uncertainty – relative to the resources used – to the Heisenberg limit.

We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev’s phase estimation algorithm, using adaptive measurement theory, in order to achieve a standard deviation scaling at the Heisenberg limit. Resources are characterized by the total number of applications of the phase shift. Experimentally, we implement the protocol using a common spatial-mode interferometer and measure a birefringent phase shift between right and left circular-polarized light, demonstrating Heisenberg-limited scaling. I also discuss simplifications of this technique that still achieve the same scaling of sensitivity.