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Minimising the heat dissipation of information erasure

Mohammady, M. ; Mohseni, M. ; Omar, Y.

Minimising the heat dissipation of information erasure, Proc QPL, Oxford, United Kingdom, Vol. N/A, pp. N/A - N/A, July, 2015.

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Quantum state engineering and quantum computation rely on procedures that, up to some fidelity, prepare a quantum object in a pure state. If the object is initially in a statistical mixture, then this
increases the largest eigenvalue of its probability spectrum. We refer to this as probabilistic infor-
mation erasure. Such processes are said to 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 energy as 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 physi-
cal context, i.e, for a specific reservoir etc. To determine the achievable minimal heat dissipation of
min-entropy reduction within a given physical context, we must explicitly optimise over all possible
unitary operators that act on the composite system of object and reservoir. In this paper we charac-
terise the equivalence class of such optimal unitary operators, using tools from majorisation theory,
when we are restricted to finite dimensional Hilbert spaces.