Extra QLunch: Tim Möbus
Speaker: Tim Möbus
Title: Energy preserving evolutions of bosonic systems
Abstract: The exponential convergence to invariant subspaces of quantum Markov semigroups plays a crucial role in quantum information theory. One such example is in bosonic error correction schemes, where dissipation is used to drive states back to the codespace - an invariant subspace protected against certain types of errors. In this paper, we investigate perturbations of quantum dynamical semigroups that operate on continuous variable (CV) systems and admit an invariant subspace.
First, we prove a generation theorem for quantum Markov semigroups on CV systems under the physical assumptions that (i) the generator has GKSL form with corresponding jump operators defined as polynomials of annihilation and creation operators; and (ii) the (possibly unbounded) generator increases all moments in a controlled manner.
Additionally, we show that the level sets of operators with bounded first moments are admissible subspaces of the evolution, providing the foundations for a perturbative analysis. Our results also extend to time-dependent semigroups. We apply our general framework to two settings of interest in continuous variables quantum information processing.
First, we provide a new scheme for deriving continuity bounds on the energy-constrained capacities of Markovian perturbations of Quantum dynamical semigroups. Second, we provide a quantitative analysis of the dampening of continuous-time evolutions generating a universal gate set for CAT-qubits outside their code-space.