As with anything involving information or communication there is a minimum amount of energy required for any measurement at a given precision.
There may be several "minimums" depending on how idealized the approach but in general the precision is proportional to the energy or power consumed.
If you need to double the SNR then you'll need to double the energy necessary for the measurement.
Has anyone done anything with this? It's hard to start a key word search other than "measurement science."
Bret Cahill