Time-energy costs of quantum measurements

Time and energy of quantum processes are a tradeoff against each other. We propose to ascribe to any given quantum process a time-energy cost to quantify how much computation it performs. Here, we analyze the time-energy costs for general quantum measurements, along a similar line as our previous work for quantum channels, and prove exact and lower bound formulas for the costs. We use these formulas to evaluate the efficiencies of actual measurement implementations. We find that one implementation for a Bell measurement is optimal in time energy. We also analyze the time-energy cost for unambiguous state discrimination and find evidence that only a finite time-energy cost is needed to distinguish any number of states.