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arXiv · 2512.02186

Absorption-based qubit estimation in discrete-time quantum walks

Edgard P. M. Amorim·Lorena R. Cerutti·O. P. de Sá Neto·M. C. de Oliveira
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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 Cram\'er-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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Edgard P. M. Amorim, Lorena R. Cerutti, O. P. de Sá Neto, M. C. de Oliveira. 2025-12-01. Absorption-based qubit estimation in discrete-time quantum walks. https://doi.org/10.1103/zns5-vzyy

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