Metrology, metastability and dynamical phase transitions in open quantum systems

Abstract

In this thesis we explore aspects of dynamics of open quantum systems related to coherence and quantum correlations - necessary resources for enhanced quantum metrology and quantum computation. We first discuss limits to the precision of parameter estimation when using a quantum system in the presence of noise. To this end we introduce a variational principle for the quantum Fisher information (QFI) bounding the estimation errors of any measurement, which motivates an efficient iterative algorithm for finding optimal system preparations for noisy estimation experiments. Furthermore, we investigate influence of noise correlations on the precision in phase and frequency estimation, by delivering bounds for both spatially and temporarily correlated (non-Markovian) dephasing noise. This allows us to prove the Zeno limit in frequency estimation, conjectured in Phys. Rev. A 84, 012103 (2011) and Phys. Rev. Lett. 109, 233601 (2012). The enhanced estimation precision in quantum metrology can be, however, achieved only using highly entangled states. We propose a scheme of generating such highly correlated states as outputs of Markovian open quantum systems near first-order dynamical phase transitions. We show that the quadratic scaling of the QFI with time is present for experiments within the correlation time of the dynamics and describe a theoretical scheme for quantum enhanced estimation of an optical phase-shift using the photons being emitted from an intermittent quantum system. Finally, we establish the basis for a theory of metastability in Markovian open quantum systems, by extending methods from classical stochastic dynamics. We argue that the partial relaxation into long-lived metastable states - distinct from the asymptotic stationary state - may preserve initial coherences within decoherence-free subspaces or noiseless subsystems, thus allowing for quantum computation during the metastable regime