RECORD
Bounding Two-Way Average Communication Cost of Simulating Quantum Correlations
Quantum Physics · Submitted 3 Oct 2026
abstract compiled · 2026-10-06 · no language-model review
The authors' main claim When applied to parallel games, these bounds yield explicit finite quantum correlations for which the exact simulation cost exceeds any prescribed finite input-average communication budget.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Bell nonlocal correlations cannot be reproduced by local hidden-variable models without communication, making classical communication cost a natural quantitative measure of nonlocality. Although finite communication always suffices to simulate any correlation in a fixed finite Bell scenario, determining the minimum amount needed to (exactly) simulate any given nonlocal correlation remains challenging, especially in the average-cost setting. Here, we derive lower bounds on input-average communication cost from nonlocal games, allowing variable-length, fully interactive two-way protocols. When applied to parallel games, these bounds yield explicit finite quantum correlations for which the exact simulation cost exceeds any prescribed finite input-average communication budget. For $n$ parallel Magic-Square-winning correlations, we prove a lower bound of $n\log_2(3/2)$ bits and give a one-way communication protocol that attains this rate asymptotically. For the quantum correlation maximally winning the $n$-copy of the Clauser--Horne--Shimony--Holt nonlocal game, we obtain an input-average lower bound of approximately $0.04627n$ bits for exact simulation. Finally, we formulate a hierarchy of lower bounds and complementary upper bounds using deterministic correlations up to chosen communication costs. Both recover the exact input-average cost at their final levels, and if the bounds agree at lower levels, their common value yields the exact input-average cost without needing to consider all communication strategies.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Bell nonlocal correlations cannot be reproduced by local hidden-variable models without communication, making classical communication cost a natural quantitative measure of nonlocality. | background 1.00 | 0.04 | 0.04 | asserted 1.00 |
| s1 | Although finite communication always suffices to simulate any correlation in a fixed finite Bell scenario, determining the minimum amount needed to (exactly) simulate any given nonlocal correlation remains challenging, especially in the average-cost setting. | gap 0.86 | 0.04 | 0.04 | asserted 0.98 |
| s2 | Here, we derive lower bounds on input-average communication cost from nonlocal games, allowing variable-length, fully interactive two-way protocols. | contribution 0.84 | 0.97 | 0.14 | asserted 1.00 |
| s3 | When applied to parallel games, these bounds yield explicit finite quantum correlations for which the exact simulation cost exceeds any prescribed finite input-average communication budget. | result 0.98 | 0.93 | 0.43 | asserted 1.00 |
| s4 | For $n$ parallel Magic-Square-winning correlations, we prove a lower bound of $n\log_2(3/2)$ bits and give a one-way communication protocol that attains this rate asymptotically. | result 0.99 | 0.96 | 0.18 | asserted 1.00 |
| s5 | For the quantum correlation maximally winning the $n$-copy of the Clauser--Horne--Shimony--Holt nonlocal game, we obtain an input-average lower bound of approximately $0.04627n$ bits for exact simulation. | result 1.00 | 0.96 | 0.11 | asserted 1.00 |
| s6 | Finally, we formulate a hierarchy of lower bounds and complementary upper bounds using deterministic correlations up to chosen communication costs. | contribution 0.73 | 0.94 | 0.10 | asserted 1.00 |
| s7 | Both recover the exact input-average cost at their final levels, and if the bounds agree at lower levels, their common value yields the exact input-average cost without needing to consider all communication strategies. | interpretation 0.42 | 0.88 | 0.15 | asserted 0.99 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Bell nonlocal correlations cannot be reproduced by local hidden-variable models without communication, making classical communication cost a natural quantitative measure of nonlocality. Although finite communication always suffices to simulate any correlation in a fixed finite Bell scenario, determining the minimum amount needed to (exactly) simulate any given nonlocal correlation remains challenging, especially in the average-cost setting. Here, we derive lower bounds on input-average communication cost from nonlocal games, allowing variable-length, fully interactive two-way protocols. When applied to parallel games, these bounds yield explicit finite quantum correlations for which the exact simulation cost exceeds any prescribed finite input-average communication budget. For $n$ parallel Magic-Square-winning correlations, we prove a lower bound of $n\log_2(3/2)$ bits and give a one-way communication protocol that attains this rate asymptotically. For the quantum correlation maximally winning the $n$-copy of the Clauser--Horne--Shimony--Holt nonlocal game, we obtain an input-average lower bound of approximately $0.04627n$ bits for exact simulation. Finally, we formulate a hierarchy of lower bounds and complementary upper bounds using deterministic correlations up to chosen communication costs. Both recover the exact input-average cost at their final levels, and if the bounds agree at lower levels, their common value yields the exact input-average cost without needing to consider all communication strategies.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.