Interferences in quantum eraser reveal geometric phases in modular and weak values

TL;DR

This paper introduces a new experimental method to fully determine complex modular values of observables in quantum systems, revealing their topological phase and its relation to quantumness.

Contribution

It presents a procedure to measure both the modulus and phase of modular values for any measurement strength in a single step using interferometry.

Findings

The phase of modular and weak values has a topological origin.

The method works for all measurement strengths and post-selected states.

The phase relates to the intrinsic properties and evolution of the quantum system.

Abstract

In this letter, we present a new procedure to determine completely the complex modular values of arbitrary observables of pre- and post-selected ensembles, which works experimentally for all measurement strengths and all post-selected states. This procedure allows us to discuss the physics of modular and weak values in interferometric experiments involving a qubit meter. We determine both the modulus and the argument of the modular value for any measurement strength in a single step, by controlling simultaneously the visibility and the phase in a quantum eraser interference experiment. Modular and weak values are closely related. Using entangled qubits for the probed and meter systems, we show that the phase of the modular and weak values has a topological origin. This phase is completely defined by the intrinsic physical properties of the probed system and its time evolution. The physical significance of this phase can thus be used to evaluate the quantumness of weak values.