Three-slit interference with a which-path memory ancilla: A bright-dark state formulation
Abstract
In this paper, we study the effect of a which-path memory ancilla on the three-slit interference pattern within the framework of the bright--dark state description [Phys. Rev. Lett. 134, 133603 (2025)]. Whereas two slits give one bright mode, a photonic mode that couples to the detector atoms, and one dark mode, which does not couple to the detector atoms, three slits lead to one detector-coupled bright mode and a two-dimensional dark-mode subspace in the three-dimensional path space. We first discuss the classical three-slit interference pattern in terms of probability leakage into the dark subspace. We then study the von Neumann entropy SD of the dark subspace and the coherence measures of the reduced photonic state obtained by tracing out the memory: dark-sector coherence CD and bright--dark coherence CBD. These quantities bring out the internal quantum structure of the two-dimensional dark subspace. We show that, whereas CD is not by itself a basis-independent physical observable, CBD is basis-invariant. We establish that, for two paths, CBD is fixed entirely by the populations and the single pairwise coherence, whereas for multiple paths, M≥ 3, it acquires a genuinely multipath contribution generated by asymmetry among the pairwise which-path overlaps. Finally, we distinguish the part of the path-coherence loss that is recoverable through a suitable measurement of the memory from the irreducible coherence deficit imposed by an uncontrolled environment.
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BibTeX
@misc{kumar2026threeslit,
title = {{Three-slit interference with a which-path memory ancilla: A bright-dark state formulation}},
author = {Ajay Kumar and Guruprasad Kadam and Anirban Pathak},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.24243},
eprint = {2608.24243},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24243},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Three-slit interference with a which-path memory ancilla: A bright-dark state formulation
AU - Ajay Kumar
AU - Guruprasad Kadam
AU - Anirban Pathak
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2608.24243
UR - https://arxiv.org/abs/2608.24243
AB - In this paper, we study the effect of a which-path memory ancilla on the three-slit interference pattern within the framework of the bright--dark state description [Phys. Rev. Lett. 134, 133603 (2025)]. Whereas two slits give one bright mode, a photonic mode that couples to the detector atoms, and one dark mode, which does not couple to the detector atoms, three slits lead to one detector-coupled bright mode and a two-dimensional dark-mode subspace in the three-dimensional path space. We first discuss the classical three-slit interference pattern in terms of probability leakage into the dark subspace. We then study the von Neumann entropy S_D of the dark subspace and the coherence measures of the reduced photonic state obtained by tracing out the memory: dark-sector coherence C_D and bright--dark coherence C_BD. These quantities bring out the internal quantum structure of the two-dimensional dark subspace. We show that, whereas C_D is not by itself a basis-independent physical observable, C_BD is basis-invariant. We establish that, for two paths, C_BD is fixed entirely by the populations and the single pairwise coherence, whereas for multiple paths, M≥ 3, it acquires a genuinely multipath contribution generated by asymmetry among the pairwise which-path overlaps. Finally, we distinguish the part of the path-coherence loss that is recoverable through a suitable measurement of the memory from the irreducible coherence deficit imposed by an uncontrolled environment.
ER -