Abstract
The number of outcomes is an intrinsic property of a quantum measurement, which has the potential to improve the performance of quantum information processing. Recently, there have been fruitful results on resource theories of quantum measurements. In this paper, we investigate the number of measurement outcomes as a kind of resource. We cast the robustness of this resource as a semi-definite positive program. Its dual problem confirms that if a measurement cannot be simulated by the measurements with a smaller number of outcomes, there exists a state discrimination task where it outperforms the latter. An upper bound of this advantage is derived, which can be saturated if the number of outcomes is smaller than the dimension of the Hilbert space. We also show that the possible tasks to reveal the advantage can be more general and not restricted to state discrimination.
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