Abstract
Quantum state engineering and quantum computation rely on information erasure procedures that, up to some fidelity, prepare a quantum object in a pure state. Such processes occur within Landauer's framework if they rely on an interaction between the object and a thermal reservoir. Landauer's principle dictates that this must dissipate a minimum quantity of heat, proportional to the entropy reduction that is incurred by the object, to the thermal reservoir. However, this lower bound is only reachable for some specific physical situations, and it is not necessarily achievable for any given reservoir. The main task of our work can be stated as the minimisation of heat dissipation given probabilistic information erasure, i.e., minimising the amount of energy transferred to the thermal reservoir as heat if we require that the probability of preparing the object in a specific pure state be no smaller than . Here is the maximum probability of information erasure that is permissible by the physical context, and the error. To determine the achievable minimal heat dissipation of quantum information erasure within a given physical context, we explicitly optimise over all possible unitary operators that act on the composite system of object and reservoir. Specifically, we characterise the equivalence class of such optimal unitary operators, using tools from majorisation theory, when we are restricted to finite-dimensional Hilbert spaces. Furthermore, we discuss how pure state preparation processes could be achieved with a smaller heat cost than Landauer's limit, by operating outside of Landauer's framework.
Highlights
Information erasure and thermodynamics In his attempt to exorcise Maxwell’s demon [1, 2], Leo Szilard conceived of an engine [3] composed of a box that is in thermal contact with a reservoir at temperature T, and contains a single gas particle
We used techniques from majorisation theory to characterise the equivalence class of unitary operators that bring the probability of information erasure to a desired value and minimise the consequent heat dissipation to the thermal reservoir
By constructing a sequential swap algorithm, we demonstrated that there is a tradeoff between the probability of information erasure and the minimal heat dissipation
Summary
Information erasure and thermodynamics In his attempt to exorcise Maxwell’s demon [1, 2], Leo Szilard conceived of an engine [3] composed of a box that is in thermal contact with a reservoir at temperature T, and contains a single gas particle. In order to save the second law of thermodynamics the engine must dissipate at least kB T log(2) units of energy to the thermal reservoir as heat. While it was initially believed that this heat dissipation is due to the measurement act by the Maxwellian demon, following the work of Landauer, Penrose, and Bennet [4,5,6,7] the responsible process was identified as the erasure of information in the demon’s memory—the logically irreversible process of assigning a prescribed value to the memory, irrespective of its prior state. Where DQ is the heat dissipation to the thermal reservoir and DS is the entropy reduction in the object of information erasure
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