A time-dependent Tsirelson's bound from limits on the rate of information gain in quantum systems
arXiv:1105.2268 · doi:10.1088/1367-2630/13/7/073033
Abstract
We consider the problem of distinguishing between a set of arbitrary quantum states in a setting in which the time available to perform the measurement is limited. We provide simple upper bounds on how well we can perform state discrimination in a given time as a function of either the average energy or the range of energies available during the measurement. We exhibit a specific strategy that nearly attains this bound. Finally, we consider several applications of our result. First, we obtain a time-dependent Tsirelson's bound that limits the extent of the Bell inequality violation that can be in principle be demonstrated in a given time t. Second, we obtain a Margolus-Levitin type bound when considering the special case of distinguishing orthogonal pure states.
15 pages, revtex, 1 figure
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