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 multitime 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 nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories.
| Original language | English |
|---|---|
| Article number | 052102 |
| Journal | Physical Review A |
| Volume | 97 |
| Issue number | 5 |
| DOIs | |
| State | Published - 3 May 2018 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2018 American Physical Society.
Funding
We wish to thank Yakir Aharonov, Bengt Svensson, and Dmitri Sokolovski for helpful comments and discussions. We also thank Alexandre Matzkin, who suggested to us some interesting literature to examine, and three anonymous referees for very helpful comments. E.C. was supported by the Canada Research Chairs (CRC) Program.
| Funders | Funder number |
|---|---|
| E.C. | |
| Canada Research Chairs | CRC |