Cros Carrillo De Albornoz, Alejandro; (2025) On Quantum Information and Superconducting Cats. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis investigates fundamental aspects of quantum systems, focusing on entanglement transitions, classification of quantum-ness, and experimental realisations of tunable quantum phenomena with applications to quantum information processing and chemical simulations. In \cref{sec_I: entanglement}, we explore entanglement and heterogeneity in random Lindbladian dynamics describing open quantum systems. By modelling a one-dimensional chain of non-interacting spinless fermions coupled to local baths with power-law decaying interactions, we demonstrate a volume-to-area law entanglement phase transition in the mixed steady state by tuning the power-law exponent $p$. This transition, stable even with coherent hopping, is exhibited by the averaged steady-state density matrix of the Lindbladian, providing theoretical insights into stabilising quantum correlations in mixed states of long-range open systems. In \cref{sec_I: macroscopicity}, we address the question of what makes a state inherently quantum by introducing a new measure called \textit{quantum macroscopicity}, $M$. Building on the Gottesman-Knill theorem, $M$ distinguishes trivial operations from genuinely quantum ones by representing states in an operator basis $\mathcal{G}$, normalised by a group of chosen trivial physical operations $\mathcal{N}(\mathcal{G})$ and calculating their entropy. Applied to spin-$\tfrac{1}{2}$ chains, $M$ captures aspects of quantum complexity beyond entanglement. In continuous variable systems, it effectively discriminates between states like cat and GKP states from coherent states regardless of photon number. This framework extends to include dissipation and measurement, offering a new tool for studying quantum error correction and computing architectures. In \cref{sec_II: cats}, we analyse an experimental realisation of a fully tunable asymmetric double-well potential using a continuously driven Kerr parametric oscillator with third-order nonlinearity. Utilising a low-noise, all-microwave control system with high-efficiency readout of well occupancy, we explore reaction rates across tunnelling resonances. We uncover two counter-intuitive effects: (i) a weak asymmetry significantly decreases activation rates even when the initial well is shallower, and (ii) the width of tunnelling resonances alternates between narrow and broad as a function of well depth and asymmetry. These findings, predicted to manifest in quantum-regime chemical double-well systems, pave the way for analogue molecular simulators based on quantum superconducting circuits. Collectively, these studies advance our understanding of quantum systems by providing theoretical frameworks and experimental techniques for controlling and measuring quantum phenomena, with implications for quantum simulation, information processing, and reaction dynamics.

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