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This research presents a rigorous theoretical framework for continuous-time quantum walks featuring absorption at boundaries modeled as non-Hermitian systems. By deriving closed-form expressions for the propagator, it reveals how strong dissipation creates localized edge modes that fundamentally alter first-passage statistics and phase-space dynamics. These findings advance our understanding of open quantum system behavior, which is critical for designing robust quantum algorithms resilient to decoherence.
Boundary-localized non-Hermitian modes in an absorbing quantum walk
arXiv:2605.08056v3 Announce Type: replace Abstract: We introduce and solve from first principles a continuous-time quantum walk with absorption generated by a Lindblad boundary sink of arbitrary strength. Tracing out the sink maps the problem onto a non-Hermitian tight-binding Hamiltonian with a rank-one imaginary defect on the semi-infinite line. We obtain closed-form expressions for the exact propagator, from which the first-passage statistics follow. Weak coupling limits absorption through inefficient transfer into the sink, whereas for strong dissipation, occupation at the boundary is stunted by the emergence of a localized non-Hermitian mode. Despite the different physical origin of these suppression mechanisms, we show their respective absorption probabilities exhibit an asymptotic duality. The evolution is conveniently visualized in phase-space, where the non-Hermitian mode produces a Wigner droplet exponentially confined near the edge site.
Abstract:We introduce and solve from first principles a continuous-time quantum walk with absorption generated by a Lindblad boundary sink of arbitrary strength. Tracing out the sink maps the problem onto a non-Hermitian tight-binding Hamiltonian with a rank-one imaginary defect on the semi-infinite line. We obtain closed-form expressions for the exact propagator, from which the first-passage statistics follow. Weak coupling limits absorption through inefficient transfer into the sink, whereas for strong dissipation, occupation at the boundary is stunted by the emergence of a localized non-Hermitian mode. Despite the different physical origin of these suppression mechanisms, we show their respective absorption probabilities exhibit an asymptotic duality. The evolution is conveniently visualized in phase-space, where the non-Hermitian mode produces a Wigner droplet exponentially confined near the edge site.
arXiv:2605.08056 [quant-ph]
(or arXiv:2605.08056v3 [quant-ph] for this version)
From: Francisco Riberi Mr. [view email] [v1] Fri, 8 May 2026 17:43:56 UTC (674 KB) [v2] Sun, 17 May 2026 22:11:43 UTC (678 KB) [v3] Mon, 17 Aug 2026 21:12:41 UTC (680 KB)
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