  It is also important to bear in mind that all attempts to derive Landauer's principle, to date, have been based upon classical information processing. While it would appear that a lower bound, very similar in form to Landauer's principle, can be derived for quantum computational operations, unlike the classical case there appears no proof as yet of the existence of processes that can in principle reach this bound. It remains possible, therefore, that quantum computations may need to incur additional thermodynamic costs. This appears to be true even for the quantum analog of logically reversible operations: Bennett's (1973) procedure for avoiding the cost of storing additional bits involves an operation which cannot in general be applied to quantum operations (Maroney 2004 [in Other Internet Resources]). Finally, as noted above, Allahverdyan and Nieuwenhuizen argued in the opposite direction, that the derivations of this lower bound involve assumptions which can be violated by quantum theory in the low temperature regime.