On the Heisenberg principle at macroscopic scales: understanding classical negative information. Towards a general physical theory of information

TL;DR

This paper explores the classical Heisenberg principle at macroscopic scales by analyzing negative information and measurement disturbance, proposing a new metric applicable to both classical and quantum systems as a foundation for a general theory of information.

Contribution

It introduces a novel transfer information content metric that unifies classical and quantum measurement disturbance, advancing towards a comprehensive physical theory of information.

Findings

Classical local mutual information can be negative due to measurement disturbance.

A new Shannon metric, transfer information content, quantifies information-disturbance trade-offs.

The metric applies to both classical and quantum measurements, linking to the Heisenberg principle.

Abstract

With the aid of a toy model, the Monty Hall Problem (MHP), the counterintuitive and theoretically problematic concept of negative information in classical systems is well understood. It is shown that, as its quantum counterpart, classical local mutual information, obtained through a measurement, can be expressed as the difference between the information gained with the evidence and the negative information generated due to the inefficiency of the measurement itself; a novel local Shannon metric, the transfer information content, is defined as this difference, which is negative if the measurement generates more disturbance than the evidence, i.e., generates a classical measurement back action. This metric is valid for both, Classical and Quantum measurements, and it is proposed as a starting point towards a general physical theory of information. This information-disturbance trade-off in classical measurements is a kind of Heisenberg principle at macroscopic scales, and it is proposed, as further work, to incorporate this result in the already existing generalized uncertainty principles in the field of quantum gravity.