Experimental investigation of the uncertainty relation in pre- and postselected systems

TL;DR

This paper experimentally investigates the Robertson-Heisenberg uncertainty relation in pre- and postselected quantum systems using weak measurements, revealing limitations on state preparation and potential applications in precision measurement techniques.

Contribution

It provides the first experimental verification of uncertainty relations in PPS systems with von Neumann measurements, advancing understanding of quantum foundations.

Findings

Uncertainty relations between incompatible observables are experimentally confirmed in PPS systems.

Limitations on joint sharp preparation of pre- and postselected states are demonstrated.

Results have implications for developing amplification techniques in precision measurements.

Abstract

Uncertainty principle is one of the fundamental principles of quantum mechanics. Exploring such uncertainty relations in pre- and postselected (PPS) systems, where weak measurements on post-selected states have been used as a powerful tool for exploring the foundation of quantum mechanics, has so far eluded experimental effort. In this work, we experimentally investigate the Robertson-Heisenberg-type uncertainty relation for two incompatible observables in a PPS system. Through conducting a von Neumann-type measurement, uncertainty relations between two non-commuting Pauli observables are experimentally unveiled. Such uncertainty relations in the PPS system impose limitations on the joint sharp preparation of pre- and postselected states for two incompatible observables. Our experiments would be useful for the development of amplification techniques for precision measurements.