The impossibility of Landauer's bound for almost every quantum state

Abstract

The thermodynamic cost of resetting an arbitrary initial state to a particular desired state is lower bounded by Landauer's bound. However, here we demonstrate that this lower bound is necessarily unachievable for nearly every initial state, for any reliable reset mechanism. Since local heating threatens rapid decoherence, this issue is of substantial importance beyond mere energy efficiency. For the case of qubit reset, we find the minimally dissipative state analytically for any reliable reset protocol, in terms of the entropy-flow vector introduced here. This allows us to verify a recent theorem about initial-state dependence of entropy production for any finite-time transformation, as it pertains to quantum state preparation.

arXiv comment9 pages plus 3 pages of appendices, 3 figures

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• Is stochastic thermodynamics the key to understanding the energy costs of computation?
• Fundamental energy cost of finite-time computing
• Finite-time Landauer principle beyond weak coupling
• Landauer Principle and Thermodynamics of Computation
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• Inverse linear versus exponential scaling of work penalty in finite-time bit reset
• Engines for predictive work extraction from memoryful quantum stochastic processes
• Generalized Zurek's bound on the cost of an individual classical or quantum computation
• Global-Local Duality of Energetic Control Cost in Multipartite Quantum Correlated Systems