Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources

Abstract

Our aim is twofold: First, we rigorously analyse the generators of quantum-dynamical semigroups of thermodynamic processes. We characterise a wide class of GKSL-generators for quantum maps within thermal operations and argue that every infinitesimal generator of (a one-parameter semigroup of) Markovian thermal operations belongs to this class. We completely classify and visualise them and their non-Markovian counterparts for the case of a single qubit. Second, we use this description in the framework of bilinear control systems to characterise reachable sets of coherently controllable quantum systems with switchable coupling to a thermal bath. The core problem reduces to studying a hybrid control system ("toy model") on the standard simplex allowing for two types of evolution: (i) instantaneous permutations and (ii) a one-parameter semigroup of $d$-stochastic maps. We generalise upper bounds of the reachable set of this toy model invoking new results on thermomajorisation. Using tools of control theory we fully characterise these reachable sets as well as the set of stabilisable states as exemplified by exact results in qutrit systems.

arXiv comment45 pages main

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Cited by in corpus (10)

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• Quantum resource-theoretical analysis of the role of vibrational structure in photoisomerization
• Finite-Dimensional Stinespring Curves Can Approximate Any Dynamics
• Bringing Quantum Systems under Control: A Tutorial Invitation to Quantum Computing and Its Relation to Bilinear Control Systems
• Almost All Quantum Channels Are Diagonalizable
• The Thermomajorization Polytope and Its Degeneracies
• Reachability, Coolability, and Stabilizability of Open Markovian Quantum Systems with Fast Unitary Control
• A universal constraint for relaxation rates for quantum Markov generators: complete positivity and beyond