Effective information bounds in modified quantum mechanics

TL;DR

This paper investigates how modifications to quantum mechanics, such as collapse models and quantum gravity effects, alter fundamental quantum limits and could be tested with high-precision experiments.

Contribution

It provides a general analysis of information bounds in modified quantum theories, revealing oscillatory effects in nonlocal models inspired by quantum gravity.

Findings

Quantum speed limits are corrected by modifications.

Heisenberg limits for parameter estimation are altered.

Oscillatory bounds may be observable in future experiments.

Abstract

A common feature of collapse models and an expected signature of the quantization of gravity at energies well below the Planck scale is the deviation from ordinary quantum-mechanical behavior. Here, we analyze the general consequences of such modifications from the point of view of quantum information theory and we anticipate applications to different quantum systems. We show that quantum systems undergo corrections to the quantum speed limit which, in turn, imply the modification of the Heisenberg limit for parameter estimation. Our results hold for a wide class of scenarios beyond ordinary quantum mechanics. For some nonlocal models inspired by quantum gravity, the bounds are found to oscillate in time, an effect that could be tested in future high-precision quantum experiments.