Axiomatic foundation of quantum measurements and survival effect

TL;DR

This paper develops an axiomatic framework for quantum measurements, revealing a survival effect in position measurements that challenges traditional uncertainty relations and suggesting new experimental tests.

Contribution

It introduces a rigorous axiomatic theory for quantum first-kind measurements, including non-ideal conditions, and uncovers the survival effect that modifies uncertainty relations.

Findings

Survival effect occurs in position but not in momentum measurements.

Survival effect violates the Heisenberg uncertainty principle.

Modified uncertainty relations can be experimentally tested.

Abstract

The axiomatic theory of quantum first-kind measurements is developed in a rigorous form based on five Postulates. The measurement theory for observable with continuous spectrum is given in a rigged Hilbert space. This approach also describes the measurements with non-ideal initial conditions. It yields the survival effect in the position measurement of the particles. It is also found that there is no such survival effect in the momentum measurement of the particles. These Postulates of axiomatic theory yield the survival effect which violates the Heisenberg uncertainty relation. This theoretical result is demonstrated by the wave function with minimum of position and momentum uncertainty of the particle. The survival effect leads to essential corrections for the uncertainty relations. These modified uncertainty relations can also be used for the experimental verification of the survival measurement effect.