No-signaling versus quantum constraints for spatio-temporal correlations caused by weak measurement

TL;DR

This paper derives a measurement uncertainty principle based on no-signaling and non-locality assumptions, providing a quantitative bound on disturbance in spatio-temporal correlations without relying on quantum formalism.

Contribution

It introduces a gentle measurement approach and derives a quantitative uncertainty relation from no-signaling and Bell inequality violations, independent of quantum theory.

Findings

Bound disturbance of observables based on information gained

Quantitative relation resembles quantum mechanical formulations

Derived without using quantum formalism

Abstract

One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty principle from two comprehensible assumptions: impossibility of instantaneous messaging at a distance (no-signaling), and violation of Bell inequalities (non-locality). The uncertainty is established for a pair of observables of one of two spatially separated systems that exhibit non-local correlations. To this end, we introduce a gentle form of measurement which acquires partial information about one of the observables. We then bound disturbance of the remaining observables by the amount of information gained from the gentle measurement, minus a correction depending on the degree of non-locality. The obtained quantitative expression resembles the quantum mechanical formulations, yet it is derived without the quantum formalism and complements the known qualitative effect of disturbance implied by non-locality and no-signaling.