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 every initial state (except possibly the single minimally dissipative input) 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.
Highlights
Whether initializing a quantum computer or a quantum experiment, a desired quantum state must be prepared
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
For any thermodynamic process that implements a nonunitary transformation of the system, the expected entropy production from time 0 through τ will depend on the initial state of the system
Summary
Whether initializing a quantum computer or a quantum experiment, a desired quantum state must be prepared. In the following, we demonstrate that no reliable protocol for preparing a quantum state can achieve Landauer’s bound for any more than, at best, one of infinitely many possible inputs to the preparation device. We find the exact minimally dissipative quantum state analytically for any reliable qubit-reset protocol, in terms of the entropy-flow vector introduced here. V, we demonstrate our results with explicit physical models for qubit erasure This allows us to verify the recent theoretical results for initial-state dependence of entropy production [Eq (9)], developed for any finite-time transformation in Ref. Even in the case of large baths, and when concerned with only average quantities, we find that Landauer’s bound still cannot be approached by more than a single initial quantum state for any reliable implementation of reset
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