Collective Quantum State Preparation Is Nonadditive
Abstract
Quantum state preparation is a basic primitive of quantum computation and control, but its resource cost is usually analyzed for one target state or under an independent-copy construction. Here we study the many-copy problem under weighted Pauli control, where a Pauli-product rotation eiϕP is charged by its rotation angle |ϕ|, independently of the weight of P. We derive the exact single-qubit preparation cost and show that it is strictly nonadditive: a four-pulse collective protocol prepares two T states at lower cost than two optimal one-copy protocols. We further identify finite regions of the Bloch sphere with collective saving, including trajectories that remain product throughout, showing that transient entanglement is not the only mechanism behind the advantage. Complementarily, a dimension-independent Rényi-entropy speed limit gives an extensive lower bound for every coherent target and an exponential fidelity penalty below a finite preparation rate. These results establish a many-copy geometry of state synthesis in which uncorrelated outputs can nevertheless benefit from collective control.
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BibTeX
@misc{zhu2026collective,
title = {{Collective Quantum State Preparation Is Nonadditive}},
author = {Lin Zhu and Ranyiliu Chen and Xin Wang and Shenggen Zheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06113},
eprint = {2610.06113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06113},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Collective Quantum State Preparation Is Nonadditive
AU - Lin Zhu
AU - Ranyiliu Chen
AU - Xin Wang
AU - Shenggen Zheng
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06113
UR - https://arxiv.org/abs/2610.06113
AB - Quantum state preparation is a basic primitive of quantum computation and control, but its resource cost is usually analyzed for one target state or under an independent-copy construction. Here we study the many-copy problem under weighted Pauli control, where a Pauli-product rotation e^iϕP is charged by its rotation angle |ϕ|, independently of the weight of P. We derive the exact single-qubit preparation cost and show that it is strictly nonadditive: a four-pulse collective protocol prepares two T states at lower cost than two optimal one-copy protocols. We further identify finite regions of the Bloch sphere with collective saving, including trajectories that remain product throughout, showing that transient entanglement is not the only mechanism behind the advantage. Complementarily, a dimension-independent Rényi-entropy speed limit gives an extensive lower bound for every coherent target and an exponential fidelity penalty below a finite preparation rate. These results establish a many-copy geometry of state synthesis in which uncorrelated outputs can nevertheless benefit from collective control.
ER -