Probing finite coarse-grained virtual Feynman histories with sequential weak values

TL;DR

This paper demonstrates that sequential weak measurements can directly probe individual virtual Feynman histories, providing new insights into quantum interference and the nature of quantum histories.

Contribution

It introduces a method to experimentally access and interpret individual virtual Feynman histories using sequential weak values, linking theory with experimental practice.

Findings

Sequential weak values sum to unity for complete sets of histories.

Weak values reveal interference effects in quantum histories.

Incompatibility of weak values for non-orthogonal histories is established.

Abstract

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multi-time projection operators for a complete set of orthogonal quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse-graining in time and establish the incompatibility of weak values for non-orthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories.