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The energy cost of measurement is an interesting fundamental question, andmay have profound implications for quantum technologies. In the context ofMaxwell's demon, it is often stated that measurement has no minimum energycost, while information has a work value, even though these statements canappear contradictory. However, as we elucidate, these statements do no refer tothe cost paid by the measuring device. Here we show that it is only when ameasuring device has access to a zero temperature reservoir - that is, never -that the measurement requires no energy. All real measuring devices pay thecost that a heat engine pays to obtain the work value of the information theyacquire.

Quantum measurement and the first law of thermodynamics: the energy cost of measurement is the work value of the acquired information