# Quantum parameter estimation and state discrimination in continuous variable quantum optics

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2021

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Bradshaw, Mark

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Exemplified by the Heisenberg uncertainty principle, quantum mechanics imposes a fundamental limit to the precision we can measure complementary properties of an object, for example position and momentum. Similarly, quantum mechanics tells us there is a limit to which we can discriminate between two quantum states that are nonorthogonal. Therefore, it is an interesting question to ask, given the laws of quantum mechanics, what exactly is the best measurement outcome we can achieve? This thesis examines various problems related to quantum state discrimination and quantum parameter estimation of continuous variable quantum states.
We first examine quantum illumination, which can be regarded as a quantum state discrimination problem, where a quantum probe state is used to determine the presence or absence of an object in a noisy environment. If we use a probe that is quantum entangled with another probe, we can obtain a better performance outcome than is possible by using a probe without entanglement. We show that the source of enhancement is due to quantum discord. We also investigate what is the best probe state when entanglement is not used (conventional illumination) and when entanglement is used (quantum illumination). We analytically prove the optimal probe for various cases, and also provide some numerical results.
We also investigate the optimal estimation of parameters that parametrise a quantum state. We provide methods of calculating the Holevo Cramer Rao bound, which is a useful quantity for quantum parameter estimation. The Holevo Cramer Rao bound not only is a good lower bound to the sum of the mean squared error, in some cases it can provide a measurement that obtains it. We consider the example of the estimation of conjugate quadrature parameters of a displacement experienced by one mode of a two-mode EPR state. We not only prove that the near-optimal measurement scheme proposed by previous authors is optimal for high squeezing, we find a different measurement that is optimal for low squeezing.
Finally, we investigate using a probabilistic amplifier for quantum state discrimination and parameter estimation for coherent states. We find that the probabilistic amplifier results in improvement in discrimination and parameter estimation of coherent states under certain conditions such as when there is a high cost associated with measuring a sample.

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Thesis (PhD)

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## DOI

10.25911/FFSZ-9232