Phase transitions in first-detection statistics of monitored long-range quantum walks
Abstract
In a quantum walk, the first-detection return probability (FDRP) characterizes salient features, determining whether the quantum walk is transient or recurrent. We study the FDRP of quantum walks on a chain where the initial site is stroboscopically monitored by a detector and the walker performs long-range hopping between sites. We assume that the hopping strength decays with the distance d as d−α and α≥ 0 and show that the power-law exponent α critically determines the behavior of the FDRP. The value α=1 separates recurrent (α<1) from transient (α>1) quantum walks through a continuous phase transition in the total detection probability. For α<1, strong long-range hopping induces localization, resulting in unit total detection probability. Instead, for α>1 the long-range walk is transient and the return probability decays algebraically as a function of time as t−β. The associated decay exponent β features nonanalytic points as a function of α. Such singularities are not exclusively determined by the low-energy spectrum, but are caused by the interference between infrared and ultraviolet energy modes induced by projective measurements, signalling the emergence of critical behavior intrinsic to the non-unitary dynamics. These dynamics are solely controlled by tuning the long-range exponent α and can thus be experimentally probed in atomic and molecular systems.
Related
- Measurement-Induced Phase Transitions and Logical-Space Localization in Floquet Monitored Clifford Circuits
- Temporal Interference from Topological Transitions in Monitored Quantum Dynamics
- Exact first-detection probability in a locally monitored solvable quantum circuit
- Dynamical Phase Transitions as Properties of the Stationary State: Analytic Results after Quantum Quenches in the Spin-1/2 XXZ Chain
- Dynamical quantum phase transitions in a pseudo-Hermitian Hamiltonian: The imbalanced-pairing Kitaev model
BibTeX
@misc{roy2026phase,
title = {{Phase transitions in first-detection statistics of monitored long-range quantum walks}},
author = {Sayan Roy and Shamik Gupta and Giovanna Morigi and Gabriele Perfetto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10510},
eprint = {2609.10510},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10510},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phase transitions in first-detection statistics of monitored long-range quantum walks
AU - Sayan Roy
AU - Shamik Gupta
AU - Giovanna Morigi
AU - Gabriele Perfetto
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10510
UR - https://arxiv.org/abs/2609.10510
AB - In a quantum walk, the first-detection return probability (FDRP) characterizes salient features, determining whether the quantum walk is transient or recurrent. We study the FDRP of quantum walks on a chain where the initial site is stroboscopically monitored by a detector and the walker performs long-range hopping between sites. We assume that the hopping strength decays with the distance d as d^−α and α≥ 0 and show that the power-law exponent α critically determines the behavior of the FDRP. The value α=1 separates recurrent (α<1) from transient (α>1) quantum walks through a continuous phase transition in the total detection probability. For α<1, strong long-range hopping induces localization, resulting in unit total detection probability. Instead, for α>1 the long-range walk is transient and the return probability decays algebraically as a function of time as t^−β. The associated decay exponent β features nonanalytic points as a function of α. Such singularities are not exclusively determined by the low-energy spectrum, but are caused by the interference between infrared and ultraviolet energy modes induced by projective measurements, signalling the emergence of critical behavior intrinsic to the non-unitary dynamics. These dynamics are solely controlled by tuning the long-range exponent α and can thus be experimentally probed in atomic and molecular systems.
ER -