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Wave-particle duality of unpolarized photons

Quantum Physics 2026-05-26 v1

Abstract

Photons in a two-path interferometer best embody wave-particle duality (WPD), which is a core concept of quantum theory. So far, the WPD relation is commonly written as V2+D21V^2+D^2 \leq 1, where VV is the interference fringe visibility and DD is path distinguishability, i.e., the distinguishability of which path a photon passed. This inequality is saturated only when the which-way marker (WWM), which embodies which-path information (WPI) via an internal degree of freedom of photons, such as polarization, is in a pure state. For mixed-state WWM, conventionally defined distinguishability underestimates the amount of WPI and thus does not saturate the WPD relation. Here, we introduce a generalized measure of distinguishability DD that properly quantifies the WPI and saturates the WPD relation for all pure- and mixed-state WWM within a purification-based framework. To this end, mixed-state WWM is treated as a result of entanglement formation between the WWM and an external degree of freedom, e.g., environment, and DD is defined so that it incorporates the total WPI shared between the WWM and the environment. We show that DD thus defined is experimentally quantifiable, independently of VV, without access to the environment. We experimentally evaluate VV and DD using true single photons generated in the completely mixed (unpolarized) state, and thus verify the saturated WPD relation.

Keywords

Cite

@article{arxiv.2605.25738,
  title  = {Wave-particle duality of unpolarized photons},
  author = {Naofumi Abe and Keiichi Edamatsu},
  journal= {arXiv preprint arXiv:2605.25738},
  year   = {2026}
}

Comments

17 pages, 4 figures