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Absorption-based qubit estimation in discrete-time quantum walks

Edgard P. M. Amorim1,*, Lorena R. Cerutti1, O. P. de Sá Neto2, and M. C. de Oliveira3,†

  • *Contact author: edgard.amorim@udesc.br
  • †Contact author: marcos@ifi.unicamp.br
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APS Open Sci. 1, 000015 – Published 4 May, 2026

DOI: https://doi.org/10.1103/zns5-vzyy

Abstract

We investigate state estimation in discrete-time quantum walks with a single absorbing boundary. Using a spectral approach, we obtain closed expressions for the escape probability as a function of the initial coin state and the boundary position, together with the corresponding classical Fisher information for a binary absorption readout. Comparison with the single-copy quantum Fisher information reveals a clear complementarity: near boundaries carry broad information about the polar (Bloch-sphere) angle of the coin state, whereas moderate or distant boundaries reveal phase-sensitive regions. Because a single boundary probes only one information direction, combining two boundary placements yields, generically, a full-rank Fisher matrix and tight joint Cramér-Rao bounds while retaining a binary measurement without mode-resolved tomography. We also discuss a restricted-readout photonic implementation in which an on-chip sink realizes the absorber, and we frame the resulting advantage as a potential reduction in measurement-setting and reconfiguration overhead for low-dimensional parameter estimation tasks in architectures where direct projective access to the coin is unavailable. Our results show that absorption in quantum walks defines an analytically tractable restricted-access primitive for coin-state estimation.

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APS Open Sci. 1, 000015– Published 4 May, 2026
Vol. 1
  • Received 1 December 2025
  • Revised 7 April 2026
  • Accepted 15 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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