Distributed Inner-Product Estimation for Continuous-Variable Quantum States
Abstract
Distributed inner product estimation (DIPE) is a fundamental task in quantum information, aiming to estimate the inner product between two unknown quantum states prepared on distributed quantum platforms. For multimode continuous-variable (CV) systems, the infinite-dimensional Hilbert space poses an additional challenge. In this work, we develop a CV-DIPE protocol using only local homodyne measurements at shared phase settings and classical communication. Under a known bound on the mean energy per mode, we derive explicit finite-sample guarantees and sufficient copy counts for estimating the full inner product to prescribed accuracy and confidence. The energy constraint yields an inverse-square truncation-bias bound, while Gaussian structure strengthens the tail control to exponential decay and improves the resulting accuracy scaling. Numerical simulations with Gaussian and non-Gaussian states illustrate the balance between truncation bias and statistical error and its dependence on mode number and energy. Our results enable independent CV platforms to benchmark their state preparations against one another, even when neither state admits a tractable classical description.
Related
- Distributed Inner Product Estimation of Continuous-Variable Quantum States
- Continuous variable distributed quantum sensing in integrated photonics
- Parametric amplification of continuous-variable entangled state for loss-tolerant quantum distributed sensing
- Exponential advantage in continuous-variable quantum state learning
- Wavelength-shifting attack on a chip-based continuous-variable quantum key distribution system
BibTeX
@misc{tang2026distributed,
title = {{Distributed Inner-Product Estimation for Continuous-Variable Quantum States}},
author = {Jun Tang and Congcong Zheng and Xutao Yu and Zaichen Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40141},
eprint = {2610.40141},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40141},
}
RIS
TY - UNPB
TI - Distributed Inner-Product Estimation for Continuous-Variable Quantum States
AU - Jun Tang
AU - Congcong Zheng
AU - Xutao Yu
AU - Zaichen Zhang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40141
UR - https://arxiv.org/abs/2610.40141
AB - Distributed inner product estimation (DIPE) is a fundamental task in quantum information, aiming to estimate the inner product between two unknown quantum states prepared on distributed quantum platforms. For multimode continuous-variable (CV) systems, the infinite-dimensional Hilbert space poses an additional challenge. In this work, we develop a CV-DIPE protocol using only local homodyne measurements at shared phase settings and classical communication. Under a known bound on the mean energy per mode, we derive explicit finite-sample guarantees and sufficient copy counts for estimating the full inner product to prescribed accuracy and confidence. The energy constraint yields an inverse-square truncation-bias bound, while Gaussian structure strengthens the tail control to exponential decay and improves the resulting accuracy scaling. Numerical simulations with Gaussian and non-Gaussian states illustrate the balance between truncation bias and statistical error and its dependence on mode number and energy. Our results enable independent CV platforms to benchmark their state preparations against one another, even when neither state admits a tractable classical description.
ER -