Distributed Inner Product Estimation of Continuous-Variable Quantum States
Abstract
Continuous-variable distributed inner product estimation (CV-DIPE) compares unknown states prepared by distant bosonic and quantum optical systems. It supports benchmarking without efficient classical descriptions or joint measurements. We develop three CV-DIPE protocols for the natural class of energy-constrained continuous-variable quantum states, based on coordinated displaced parity, coordinated Haar measurements, and independent homodyne shadows. For arbitrary multimode inputs in this class, including entangled and non-Gaussian states, we establish truncation error bounds and worst-case sample complexity guarantees for the exact inner product. The leading terms of these bounds favor coordinated Haar measurements, whose global implementation is experimentally challenging. The three protocols provide certified inner product estimates for distributed continuous-variable systems from local measurement data.
Related
- Distributed Inner-Product Estimation for Continuous-Variable Quantum States
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- Exponential advantage in continuous-variable quantum state learning
- Wavelength-shifting attack on a chip-based continuous-variable quantum key distribution system
BibTeX
@misc{wang2026distributed,
title = {{Distributed Inner Product Estimation of Continuous-Variable Quantum States}},
author = {Kun Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39912},
eprint = {2610.39912},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39912},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Distributed Inner Product Estimation of Continuous-Variable Quantum States
AU - Kun Wang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39912
UR - https://arxiv.org/abs/2610.39912
AB - Continuous-variable distributed inner product estimation (CV-DIPE) compares unknown states prepared by distant bosonic and quantum optical systems. It supports benchmarking without efficient classical descriptions or joint measurements. We develop three CV-DIPE protocols for the natural class of energy-constrained continuous-variable quantum states, based on coordinated displaced parity, coordinated Haar measurements, and independent homodyne shadows. For arbitrary multimode inputs in this class, including entangled and non-Gaussian states, we establish truncation error bounds and worst-case sample complexity guarantees for the exact inner product. The leading terms of these bounds favor coordinated Haar measurements, whose global implementation is experimentally challenging. The three protocols provide certified inner product estimates for distributed continuous-variable systems from local measurement data.
ER -