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

The energy cost of measurement is an important fundamental question, and may have profound implications for quantum technologies. In the context of Maxwell's demon, it is often stated that measurement has no minimum energy cost, while information has a work value. However, as we elucidate, the first of these statements does not refer to the cost paid by the measuring device. Here we show that it is only when a measuring device has access to a zero-temperature reservoir—that is, never—that measurement requires no energy. To obtain a given amount of information, all measuring devices must pay a cost equal to that which a heat engine would pay to obtain the equivalent work value of that information.