  Landauer's principle introduces a symmetry between computational and physical
processes: erasure of information, a logically irreversible operation, must be
underlain by an irreversible transformation dissipating energy. Monitoring
micro- and nano-systems needs to enter into the energetic balance of their
control; hence, finding the ultimate limits is instrumental to the development
of future thermal machines operating at the quantum level. We report on the
experimental investigation of a bound to the irreversible entropy associated to
generalized quantum measurements on a quantum bit. We adopted a quantum
photonics gate to implement a device interpolating from the weakly disturbing
to the fully invasive and maximally informative regime. Our experiment prompted
us to introduce a bound taking into account both the classical result of the
measurement and the outcoming quantum state; unlike previous investigation, our
new entropic bound is based uniquely on measurable quantities. Our results
highlight what insights the information-theoretic approach can provide on
building blocks of quantum information processors.
