Bosonic unstructured search: quantum enhancement without entanglement
Abstract
We consider unstructured search using multimode bosonic quantum systems under energy constraints. The task is to locate an unknown marked mode among N possibilities using arbitrary control, subject to a time-averaged mean-boson-number budget nb≫ 1. We analyze a continuous-time phase-shift oracle of strength B0, with cost given by the total oracle time, and a discrete oracle with fixed phase ϕ0, with cost given by the number of queries. We give algorithms that identify the target with query complexity O(√N/nbB0) for continuous-time oracles or O(√N/nb |sin(ϕ0/2)|) for discrete oracles with nb |sin(ϕ0/2)|=O(1). In contrast, for discrete oracles with nb |sin(ϕ0/2)|=Ω(1), we provide an algorithm using O(max{1,√(N/nb|sin(ϕ0/2)|)}) queries. We also prove matching lower bounds on the query complexity, showing that these algorithms are asymptotically optimal. Furthermore, we show that, in the absence of loss, non-Gaussianity is necessary to achieve the optimal joint query scaling in N and nb, but entanglement is not. Under uniform boson loss at rate γ, we prove a query lower bound of Ω( γN / n b B02 ), attained for γ= Ω(B0 √(n b/N)) using coherent-state probes. Finally, we propose experimental implementations using multipass optical microscopy or superconducting circuits as potential routes to speeding up imaging or device calibration with a low boson-number budget.
Related
- Enhancement of Gravitationally Induced Entanglement via Quantum Squeezing
- Cavity-QED enhancement of quantum entanglement and battery performance in double quantum dots
- Nonlinear quantum multi-spin dynamics without entanglement
- Nonlocality without entanglement for multipartite quantum measurements
- Efficient capacity-achieving entanglement generation with application to pure-loss Bosonic channels
BibTeX
@misc{wang2026bosonic,
title = {{Bosonic unstructured search: quantum enhancement without entanglement}},
author = {Yu-Xin Wang and Erfan Abbasgholinejad and Supratik Sarkar and Sharoon Austin and Andrew M. Childs and Alexey V. Gorshkov and Mohammad Hafezi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17163},
eprint = {2610.17163},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17163},
}
RIS
TY - UNPB
TI - Bosonic unstructured search: quantum enhancement without entanglement
AU - Yu-Xin Wang
AU - Erfan Abbasgholinejad
AU - Supratik Sarkar
AU - Sharoon Austin
AU - Andrew M. Childs
AU - Alexey V. Gorshkov
AU - Mohammad Hafezi
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17163
UR - https://arxiv.org/abs/2610.17163
AB - We consider unstructured search using multimode bosonic quantum systems under energy constraints. The task is to locate an unknown marked mode among N possibilities using arbitrary control, subject to a time-averaged mean-boson-number budget n_b≫ 1. We analyze a continuous-time phase-shift oracle of strength B_0, with cost given by the total oracle time, and a discrete oracle with fixed phase ϕ_0, with cost given by the number of queries. We give algorithms that identify the target with query complexity O(√N/n_bB_0) for continuous-time oracles or O(√N/n_b |sin(ϕ_0/2)|) for discrete oracles with n_b |sin(ϕ_0/2)|=O(1). In contrast, for discrete oracles with n_b |sin(ϕ_0/2)|=Ω(1), we provide an algorithm using O(max{1,√(N/n_b|sin(ϕ_0/2)|)}) queries. We also prove matching lower bounds on the query complexity, showing that these algorithms are asymptotically optimal. Furthermore, we show that, in the absence of loss, non-Gaussianity is necessary to achieve the optimal joint query scaling in N and n_b, but entanglement is not. Under uniform boson loss at rate γ, we prove a query lower bound of Ω( γN / n _b B_0^2 ), attained for γ= Ω(B_0 √(n _b/N)) using coherent-state probes. Finally, we propose experimental implementations using multipass optical microscopy or superconducting circuits as potential routes to speeding up imaging or device calibration with a low boson-number budget.
ER -