A time-dependent Tsirelson's bound from limits on the rate of information gain in quantum systems

TL;DR

This paper establishes bounds on quantum state discrimination within limited time frames, linking measurement duration to energy constraints, and derives a time-dependent Tsirelson's bound affecting Bell inequality violations.

Contribution

It introduces a novel time-dependent Tsirelson's bound based on energy-limited measurement durations, with strategies nearly reaching these bounds and applications to Bell inequalities.

Findings

Derived upper bounds on quantum state discrimination in limited time.

Established a time-dependent Tsirelson's bound for Bell inequality violations.

Provided a measurement strategy that nearly attains the theoretical bounds.

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.