Minimising the heat dissipation of information erasure

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 information 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 physical 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 characterise the equivalence class of such optimal unitary operators, using tools from majorisation theory, when we are restricted to finite dimensional Hilbert spaces.