Distributed Quantum Property Testing with Quantum Carrier Pigeons

Abstract

We introduce a framework for distributed quantum inference under communication constraints. In our model, m distributed nodes each receive one copy of an unknown d-dimensional quantum state ρ, before communicating via a constrained one-way communication channel with a central node, which aims to infer some property of ρ. This framework generalizes the classical distributed inference framework introduced by Acharya, Canonne, and Tyagi [COLT 2019], by allowing quantum resources such as quantum communication and shared entanglement. Within this setting, we focus on the fundamental problem of quantum state certification: Given a complete description of some state σ, decide whether ρ=σ or |ρ−σ|₁≥ ε. Additionally, we focus on the case of limited communication between distributed nodes and the central node: we assume each communication channel is limited to only n_c bits and n_q qubits with n_c + n_q ≤ log d. When all nodes can make use of a shared source of randomness, we show that the copy complexity of distributed state certification is Θ(d²/(2^n_q 2^n_c/2ε²)). We further demonstrate that shared randomness is necessary to achieve the above complexity, by proving an Ω(d³/(4^n_q 2^n_c ε²)) lower bound in the private−coin setting. Moreover, we develop a private-coin algorithm that matches this bound up to a √(log d) factor, showing this complexity is near-optimal. Together, our work establishes a general framework for distributed quantum inference with communication constraints and characterizes the complexity of distributed state certification with limited communication.

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BibTeX RIS

BibTeX

@misc{chen2026distributed,
  title = {{Distributed Quantum Property Testing with Quantum Carrier Pigeons}},
  author = {Kenny Chen and Mina Doosti and Ryan Sweke and Chirag Wadhwa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08864},
  eprint = {2609.08864},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08864},
}

RIS

TY  - UNPB
TI  - Distributed Quantum Property Testing with Quantum Carrier Pigeons
AU  - Kenny Chen
AU  - Mina Doosti
AU  - Ryan Sweke
AU  - Chirag Wadhwa
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08864
UR  - https://arxiv.org/abs/2609.08864
AB  - We introduce a framework for distributed quantum inference under communication constraints. In our model, m distributed nodes each receive one copy of an unknown d-dimensional quantum state ρ, before communicating via a constrained one-way communication channel with a central node, which aims to infer some property of ρ. This framework generalizes the classical distributed inference framework introduced by Acharya, Canonne, and Tyagi [COLT 2019], by allowing quantum resources such as quantum communication and shared entanglement. Within this setting, we focus on the fundamental problem of quantum state certification: Given a complete description of some state σ, decide whether ρ=σ or |ρ−σ|_1≥ ε. Additionally, we focus on the case of limited communication between distributed nodes and the central node: we assume each communication channel is limited to only n_c bits and n_q qubits with n_c + n_q ≤ log d. When all nodes can make use of a shared source of randomness, we show that the copy complexity of distributed state certification is Θ(d^2/(2^n_q 2^n_c/2ε^2)). We further demonstrate that shared randomness is necessary to achieve the above complexity, by proving an Ω(d^3/(4^n_q 2^n_c ε^2)) lower bound in the private−coin setting. Moreover, we develop a private-coin algorithm that matches this bound up to a √(log d) factor, showing this complexity is near-optimal. Together, our work establishes a general framework for distributed quantum inference with communication constraints and characterizes the complexity of distributed state certification with limited communication.
ER  -

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