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. Firstly, 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. Secondly, we obtain a Margolus–Levitin type bound when considering the special case of distinguishing orthogonal pure states.
Highlights
Entropic measures tell us how much information a quantum register E contains about some classical register X in principle
As we will explain in detail below, this measure is directly related [1] to the probability of success in state discrimination [2,3,4,5,6]
Since the Margolus-Levitin theorem provides a bound on the speed of evolution, it clearly provides a bound on the minimum amount of time that is required to obtain the optimal success probability for state discrimination
Summary
Entropic measures tell us how much information a quantum register E contains about some classical register X in principle. We derive bounds on the amount of information available after a given time t. As we will explain in detail below, this measure is directly related [1] to the probability of success in state discrimination [2,3,4,5,6]. We focus on bounding the probability of success in distinguishing states {ρx}x∈X where we are given ρx with probability px. Let Pguess(X|E)H,t denote this success probability after time t when using a particular Hamiltonian H in the measurement process. After providing a more careful discussion of the measurement process, we show the following results
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