Finite Nonsignalling Resources Suffice to Simulate Entangled Qubits
Abstract
A longstanding question in Bell nonlocality is whether finite-alphabet nonsignalling resources can reproduce the continuum of measurement correlations of partially entangled qubits. Here we resolve this problem by showing that every fixed pure two-qubit state admits an exact simulation of all local projective-measurement statistics using shared randomness and finitely many Popescu-Rohrlich (PR) boxes, without communication or postselection. The boxes operate in parallel, with a worst-case bound independent of the measurement settings: at most 128cot4θ calls for the Schmidt state cosθ|00⟩+sinθ|11⟩, 0<θ<π/4. The key is an exact finite-selection method that reduces input-dependent continuous sampling to a choice from a fixed-length shared random list, implemented through a finite PR-box network. The construction extends to arbitrary mixed two-qubit states and local binary-outcome POVMs. This reveals a fundamental separation between the continuity of quantum measurement correlations and the alphabet size of the resources needed to simulate them, shedding light on the resource-theoretic structure of Bell nonlocality.
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BibTeX
@misc{tang2026finite,
title = {{Finite Nonsignalling Resources Suffice to Simulate Entangled Qubits}},
author = {Ziao Tang and Xin Wang and Ge Bai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32319},
eprint = {2610.32319},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32319},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite Nonsignalling Resources Suffice to Simulate Entangled Qubits
AU - Ziao Tang
AU - Xin Wang
AU - Ge Bai
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32319
UR - https://arxiv.org/abs/2610.32319
AB - A longstanding question in Bell nonlocality is whether finite-alphabet nonsignalling resources can reproduce the continuum of measurement correlations of partially entangled qubits. Here we resolve this problem by showing that every fixed pure two-qubit state admits an exact simulation of all local projective-measurement statistics using shared randomness and finitely many Popescu-Rohrlich (PR) boxes, without communication or postselection. The boxes operate in parallel, with a worst-case bound independent of the measurement settings: at most 128cot^4θ calls for the Schmidt state cosθ|00⟩+sinθ|11⟩, 0<θ<π/4. The key is an exact finite-selection method that reduces input-dependent continuous sampling to a choice from a fixed-length shared random list, implemented through a finite PR-box network. The construction extends to arbitrary mixed two-qubit states and local binary-outcome POVMs. This reveals a fundamental separation between the continuity of quantum measurement correlations and the alphabet size of the resources needed to simulate them, shedding light on the resource-theoretic structure of Bell nonlocality.
ER -