Absorption-based qubit estimation in discrete-time quantum walks
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| Format: | Preprint |
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2025
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| _version_ | 1866914533074796544 |
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| author | Amorim, Edgard P. M. Cerutti, Lorena R. Neto, O. P. de Sá de Oliveira, M. C. |
| author_facet | Amorim, Edgard P. M. Cerutti, Lorena R. Neto, O. P. de Sá de Oliveira, M. C. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_02186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absorption-based qubit estimation in discrete-time quantum walks Amorim, Edgard P. M. Cerutti, Lorena R. Neto, O. P. de Sá de Oliveira, M. C. Quantum Physics 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. |
| title | Absorption-based qubit estimation in discrete-time quantum walks |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.02186 |