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Metadata 
bibkey: wisemansteinberghallaji2023weakvalue
authors: H. M. Wiseman, A. M. Steinberg, M. Hallaji
year: 2023
title: Obtaining a single-photon weak value from experiments using a strong (many-photon) coherent state
doi: 10.1116/5.0137579
url: https://arxiv.org/abs/2211.15761v2
claim: "Section V conjectures that the weak value post-selected on detecting m photons exceeds the no-click weak value by precisely m times the single-photon weak value."
strata_touched:
  - D5/S3/Quantum/PassiveFockModel
  - D5/S3/Quantum/ResolvedCountWeakValue
license: citation-only
triage: anchor

Verified locator

DOI: 10.1116/5.0137579 Source: https://arxiv.org/abs/2211.15761v2 AVS Quantum Science 5, 024401 (2023). The arXiv v2 PDF states the conjecture in Section V, page 6.

Source statement

Section V, page 6: “This supports earlier approximate results which suggested that if a photon-number resolving detector were used, the weak value post-selected on detecting m photons would exceed the no-click weak value by precisely m times the single-photon number. We leave a rigorous proof of this conjecture for future work.”

The complex weak value uses the generalized postselection effect of Eq. (2). For a number-resolving detector the effect is the projector onto m photons in the detected mode, tensored with the identity on the ignored modes. The single-photon value uses the same passive network and the same probed mode, conditioned on one detected photon. Eq. (6) specifies coherent states; Eq. (7) specifies a coherent amplitude in one input mode and vacuum in the other modes.

Scope

The formal model has an arbitrary finite number of modes, each with an unbounded occupation coordinate. It retains nonzero-probability hypotheses on conditional weak values and includes the zero-count branch. Infinite mode spaces, finite-strength measurements, dark counts and the factorial-moment generating function are separate questions. The bounded literature screen recorded in issue #17772 found no prior all-count settlement; completeness remains ASSUMED-UNVERIFIED.