Temporal quantum correlations and their applications in quantum metrology

The quest to develop and implement techniques that enable the achievement of highly accurate measurements in the estimation of parameters constitutes a crucial component of the field of quantum metrology. Using quantum properties to enhance parameter estimation, the interferometry process requires the development of entangled quantum states and single-shot measurements to extract information about an unknown parameter. Despite its perceived effectiveness, implementing this scheme in a larger number of states is quite challenging. According to recent research, quantum jump metrology offers an alternative method for acquiring information. Using quantum feedback and continuous observation of an open quantum system, this method generates phase-dependent temporal correlations without the need for entanglement as a resource. This study investigates relative phase measurements in an optical network with two cavities and laser-pulse quantum feedback. The methodology proposed in the study is capable of surpassing the standard quantum limit without requiring complex quantum states. Furthermore, the discovery that quantum systems can generate not only local but also temporal non-classical correlations has been the subject of extensive research, along with the search for the most effective quantum devices that exploit these correlations. By analysing the parametrization of the two-cavity metrology scheme, it is possible to observe the analogy between the quantum jump metrology scheme and the formalism of the hidden quantum Markov models. As first steps towards investigating the quantum jump metrology scheme in the hidden quantum Markov formalism, we begin by characterising the main properties of a one-qubit hidden quantum Markov model. Comparing this machine to its classical counterpart with a single bit, a so-called hidden Markov model, we find that hidden quantum Markov model is capable of generating complex stochastic sequences and time correlations more than a single bit hidden Markov model.