Nonlocal and quantum advantages in network coding for multiple access channels

Ashutosh Rai; Hyun-Young Park; Jiyoung Yun; Joonwoo Bae; Seung-Hyun Nam; Si-Hyeon Lee

arxiv: 2304.10792 · v3 · submitted 2023-04-21 · 🪐 quant-ph · physics.app-ph

Nonlocal and quantum advantages in network coding for multiple access channels

Jiyoung Yun , Seung-Hyun Nam , Hyun-Young Park , Ashutosh Rai , Si-Hyeon Lee , Joonwoo Bae This is my paper

Pith reviewed 2026-05-24 09:35 UTC · model grok-4.3

classification 🪐 quant-ph physics.app-ph

keywords multiple-access channelnonlocal correlationsquantum resourcesnetwork codingsum capacityCHSH gamemagic square gamecooperative encoding

0 comments

The pith

Preshared nonlocal correlations and quantum resources allow senders to achieve higher sum capacities over multiple-access channels than shared randomness alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies two-sender one-receiver communication over discrete memoryless multiple-access channels without feedback. Senders may cooperate on encoding by sharing randomness, quantum states, or nonlocal correlations. For channels built from nonlocal games, the authors derive a computable lower bound on sum capacity and compute exact sum capacities in specific cases. They show that nonclassical resources produce strictly higher sum capacities than local resources. A reader would care because the result identifies concrete settings where quantum or nonlocal resources improve classical communication rates.

Core claim

When senders use cooperative encoding with quantum states or nonlocal correlations on multiple-access channels constructed by reference to nonlocal games, the resulting sum capacity exceeds the sum capacity obtained with local resources such as shared randomness. The Clauser-Horne-Shimony-Holt and magic square games yield explicit channels where this separation holds, and a general lower bound on the sum capacity is obtained from specific nonlocal and quantum strategies.

What carries the argument

Cooperative encoding that exploits preshared nonlocal correlations or quantum entanglement to induce correlated noise on codewords, producing an enlarged capacity region for the multiple-access channel.

If this is right

The sum capacity is strictly larger when senders apply nonlocal strategies derived from the CHSH game than when they use only shared randomness.
The same strict increase holds for the channel constructed from the magic square game.
A lower bound on the sum capacity is obtained directly from the value of the nonlocal game and is achievable with corresponding encoding strategies.
The capacity region for quantum and nonlocal cooperative encoding properly contains the region for local cooperative encoding.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same construction technique may produce quantum advantages in other classical network coding tasks that tolerate engineered correlated errors.
Identifying additional families of channels where nonlocal games induce useful noise patterns would extend the set of communication problems that benefit from nonclassical resources.
Experimental realizations of the game-derived channels could test whether the predicted rate gains appear in physical systems.

Load-bearing premise

The multiple-access channels must be constructed by referring to nonlocal games so that correlated noise other than independent errors occurs on the code words.

What would settle it

An explicit computation of the sum capacity for the CHSH-game or magic-square-game channel showing that the value achieved with nonlocal or quantum encoding equals or falls below the value achieved with local resources would falsify the claimed advantage.

read the original abstract

In this work, we consider two-sender, one-receiver communication over a discrete memoryless multiple-access channel without feedback, where two senders may cooperate on channel coding by using preshared resources, such as shared randomness, quantum states and measurements, or nonlocal correlations. We present the capacity region when senders employ cooperative encoding with quantum and nonlocal resources, extending beyond shared randomness, and derive a sum rate that serves as a lower bound to the sum capacity; the lower bound is computable by exploiting specific strategies. We also compute the sum capacities for two instances. One is when senders apply local resources for cooperative encoding. The other is when senders exploit nonclassical resources for encoding against channels constructed by referring to nonlocal games; in this way, correlated noise other than independent errors occurs on code words. Comparing the exact sum capacities and lower bounds, we show that nonlocal and quantum resources for cooperative encoding enable higher sum capacities over local ones. The Clauser-Horne-Shimony-Holt and magic square games are considered for constructing multiple-access channels, and we demonstrate the usefulness of nonlocal and quantum resources to achieve higher-sum capacities.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives explicit sum-capacity separations showing quantum and nonlocal encoding beat local resources on MACs built from CHSH and magic-square games.

read the letter

The main thing to know is that the authors build two concrete MACs from nonlocal games so that nonclassical cooperative encoding strictly raises the sum capacity over what local or shared-randomness strategies can achieve on the same channel. They also give a general lower bound on the sum rate that comes from explicit strategies and is computable without free parameters. For the CHSH and magic-square cases they compute the exact sum capacities on both sides and show the gap. That is the new piece: a direct, game-derived example where the separation is visible in the numbers rather than left as an existence claim. The construction is standard but the explicit comparison is cleaner than most prior shared-randomness work. The capacity region statement for quantum encoding is stated cleanly and the lower-bound strategy is described as coming from the game-winning correlations, which keeps the argument self-contained. The soft spot is that the channels are deliberately chosen to have the correlated noise the games produce, so the advantage is shown only for these instances; nothing in the abstract indicates the result extends to arbitrary MACs. The derivations themselves look internally consistent from the description, with no visible circularity or hidden fitting. This is for people who already work on quantum network information theory and want concrete capacity examples with nonclassical resources. It is worth sending to a serious referee because the explicit computations can be checked and the separation is falsifiable once the full derivations are on the table.

Referee Report

0 major / 2 minor

Summary. The manuscript considers two-sender, one-receiver discrete memoryless MACs without feedback. Senders may cooperate via preshared resources (shared randomness, quantum states/measurements, or nonlocal correlations) for encoding. It derives the capacity region under quantum/nonlocal resources, supplies a computable lower bound on sum capacity obtained from explicit strategies, computes exact sum capacities for the local-resource case and for two game-derived channels (CHSH and magic-square constructions that induce correlated noise), and shows that the nonclassical strategies achieve strictly higher sum rates than local ones.

Significance. If the explicit capacity computations and strategy constructions hold, the paper supplies concrete, falsifiable examples of quantum and nonlocal advantages in a multi-user network-coding setting. The approach of embedding nonlocal games into MAC transition probabilities to create correlated noise is a standard and internally consistent method for separating classical from nonclassical performance; the resulting proof-by-example strengthens the literature on quantum network information theory.

minor comments (2)

[capacity region derivation] § on capacity region: the statement that the lower bound 'is computable by exploiting specific strategies' would benefit from an explicit pointer to the section or algorithm that evaluates the bound for the CHSH and magic-square instances.
[abstract and introduction] The abstract and introduction should clarify whether the reported sum capacities are achieved with finite block length or in the asymptotic limit; this affects how the numerical comparisons are interpreted.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, including the summary of our results on capacity regions and sum capacities for MACs with nonlocal and quantum resources, as well as the significance of the game-based constructions for demonstrating advantages. The recommendation for minor revision is noted. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained via explicit constructions

full rationale

The paper defines specific MACs by direct reference to known nonlocal games (CHSH, magic square) and computes exact sum capacities plus explicit-strategy lower bounds for both local and nonclassical encoding on those fixed channels. All comparisons are performed on these concrete instances without parameter fitting, self-referential definitions, or load-bearing self-citations that reduce the claimed separation to the inputs by construction. This is a standard proof-by-example result whose central claims remain independently verifiable from the stated strategies and channel definitions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; all claims rest on standard information-theoretic definitions of capacity regions and the construction of channels from nonlocal games.

pith-pipeline@v0.9.0 · 5748 in / 878 out tokens · 22778 ms · 2026-05-24T09:35:17.979831+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We present the capacity region when senders employ cooperative encoding with quantum and nonlocal resources... CHSH and magic square games are considered for constructing multiple-access channels
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

sum-capacity C^(R)(N) = max_π max_E I(A1,...,An;B)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages

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The PR-box correlation is given by P(m′ 1, m′ 2|m1, m2) = 1 2 δ(m1m2, m′ 1⊕m′ 2)

No-signaling sum capacity We consider a no-signaling encoding generated via the E∗ mapping of PR-box correlation (CHSH Bell scenario). The PR-box correlation is given by P(m′ 1, m′ 2|m1, m2) = 1 2 δ(m1m2, m′ 1⊕m′ 2). We generate the encoding for the chan- nel by applying the mapping E∗ to the PR-box correl- ation. We ﬁnd that such an encoding satisfy, for...

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and that from A2 as x22 = ( a0 2, a1 2, a2 2). Then the winning condition of the game is that: (i) parity of answer of A1 is even, i.e., a0 1⊕ a1 1⊕ a2 1 = 0, (ii) parity of answer of A2 is odd, i.e., a0 2⊕ a1 2⊕ a2 2 = 1, and (iii) at the overlapping position determined by the question pair (x11, x21) the answer bit of both the players should match, i.e....

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Upper bound on classical sum capacities In a magic square game, with any local deterministic (classical) protocol the game can be won for at most eight out of nine possible questions to the two players, i.e., rmax = ω⋆ L ∆ = 8 9× 9 = 8. Therefore, the upper bound on classical sum capacity is following C (L)(NMS)≤ max π(m) { H(M)+(log 9− f (9, η)) max i,j∈...

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The quantum correlation box we consider is from Brassard et al

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Similarly, A2’s two bit outcome is assigned to (a0 2, a1

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Then it follows that with the considered quantum protocol the magic square game can be won with perfect probability, i.e., ω = 1

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(43) where we recall that Mrmax denotes a two partition M =Mrmax∪ (Mrmax )c such that|Mrmax| = rmax

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[1] [1]

Resource independent upper bound on sum capacities Proposition 4. For the MAC channelsNG, for any arbitrary encoding and probability distribution over the message set, we have the following resource independent upper bound on sum-rate I(M; Y)≤ log ∆− fW, ( 13) where equality holds if H(Y) = log ∆, ω = 1, and I(M; Y) = I(X; Y). Naturally, the stated bound ...

work page

[2] [2]

Resource dependent upper bound on sum capacity Proposition 5. For the MAC channelsNG with probability distribution π(m) over message and encodings E∈R we have a following resource dependent upper bound on sum- capacities: C (R)(NG)≤max π(m) { H(X)+( fL− fW ) max E∈R ω } − fL. ( 15) Proof. C (R)(NG) = max π(m) { max E∈R I(M; Y) } , ≤ max π(m) { max E∈R I(X...

work page

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OxNWMMW8gio5nPun+01zUjW0INo=

Upper bound on classical sum capacity Let us considerR = L; the set of local (classical) correl- ations. The set L forms a polytope (a convex set), with a set of vertices VL, in a ﬁnite dimensional Euclidean space. For an arbitrarily ﬁxed distribution π(m), I(M; Y) is a convex function of encoding E∈ L (see [18]). Therefore, given a π(m), since L is a con...

work page

[4] [4]

Computation of classical sum capacities We computed the exact classical sum capacities by performing optimization of I(M; Y) over all the vertices of the local polytope L of the CGLMP- 4 scenario, the results are plotted and shown as the lowest (dashed blue) curve in the Fig. 5

work page

[5] [5]

Lower and upper bounds on quantum sum capacities We computed a lower bound on quantum sum ca- pacities by considering a quantum encoding generated via the E∗ mapping of correlation box from the CHSH Bell scenario. The quantum correlation box we consider is the one resulting from a maximally entangled state 10 0.0 0.2 0.4 0.6 0.8 1.0 η0.0 0.5 1.0 1.5 2.0 C...

work page

[6] [6]

The PR-box correlation is given by P(m′ 1, m′ 2|m1, m2) = 1 2 δ(m1m2, m′ 1⊕m′ 2)

No-signaling sum capacity We consider a no-signaling encoding generated via the E∗ mapping of PR-box correlation (CHSH Bell scenario). The PR-box correlation is given by P(m′ 1, m′ 2|m1, m2) = 1 2 δ(m1m2, m′ 1⊕m′ 2). We generate the encoding for the chan- nel by applying the mapping E∗ to the PR-box correl- ation. We ﬁnd that such an encoding satisfy, for...

work page

[7] [7]

and that from A2 as x22 = ( a0 2, a1 2, a2 2). Then the winning condition of the game is that: (i) parity of answer of A1 is even, i.e., a0 1⊕ a1 1⊕ a2 1 = 0, (ii) parity of answer of A2 is odd, i.e., a0 2⊕ a1 2⊕ a2 2 = 1, and (iii) at the overlapping position determined by the question pair (x11, x21) the answer bit of both the players should match, i.e....

work page

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Therefore, the upper bound on classical sum capacity is following C (L)(NMS)≤ max π(m) { H(M)+(log 9− f (9, η)) max i,j∈{0,1,2} {1−π1(i)π2(j)} } − log(9)

Upper bound on classical sum capacities In a magic square game, with any local deterministic (classical) protocol the game can be won for at most eight out of nine possible questions to the two players, i.e., rmax = ω⋆ L ∆ = 8 9× 9 = 8. Therefore, the upper bound on classical sum capacity is following C (L)(NMS)≤ max π(m) { H(M)+(log 9− f (9, η)) max i,j∈...

work page

[9] [9]

The quantum correlation box we consider is from Brassard et al

Quantum sum capacities We ﬁnd the quantum sum capacities on considering a quantum encoding generated via the E∗ mapping of cor- relation box from the (2, 3, 8) Bell scenario. The quantum correlation box we consider is from Brassard et al. [15]. The two players A1 and A2 share a four qubit entangled state |Ψ⟩A1 A2 = 1 2 ( |00⟩A1|11⟩A2−| 01⟩A1|10⟩A2 −|10⟩A1...

work page

[10] [10]

Similarly, A2’s two bit outcome is assigned to (a0 2, a1

and the third bit a2 1 is given a value such that the even parity condition is satisﬁed. Similarly, A2’s two bit outcome is assigned to (a0 2, a1

work page

[11] [11]

Then it follows that with the considered quantum protocol the magic square game can be won with perfect probability, i.e., ω = 1

and the third bit a2 2 is given a value such that the odd parity condition is satisﬁed. Then it follows that with the considered quantum protocol the magic square game can be won with perfect probability, i.e., ω = 1. Therefore, magic square game is a quantum pseudo telepathy game as shown in [ 15]. Let us call the correlation box generated with considere...

work page

[12] [12]

(43) where we recall that Mrmax denotes a two partition M =Mrmax∪ (Mrmax )c such that|Mrmax| = rmax

Upper bound on classical sum capacities In a MPP nonlocal game, with any local determin- istic (classical) protocol the maximum success prob- ability, for a uniform distribution of questions, is ω⋆ L = 3 4 + 2−(⌈n/2⌉+1), therefore rmax = ω⋆ L ∆ ={ 3 4 + 2−(⌈n/2⌉+1) } × 2n and the upper bound on clas- sical sum capacity is following C (L)(NMPP )≤ max π(m) ...

work page

[13] [13]

The quantum correlation box we consider is from quantum protocol of Brassard et al

Quantum sum capacities We ﬁnd the quantum sum capacities on considering a quantum encoding generated via the E∗ mapping of correlation box from the (n, 2, 2) Bell scenario. The quantum correlation box we consider is from quantum protocol of Brassard et al. [15]. The n players A1,..., An share entangled state 1√ 2|0n⟩ + 1√ 2|1n⟩. After receiving input xk1 ...

work page 2023

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Bennett and S.J

C.H. Bennett and S.J. Wiesner, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett. 69, 2881 (1992)

work page 1992

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Bennett, P .W

C.H. Bennett, P .W. Shor, J.A. Smolin, and A.V . Thap- liyal, Entanglement-assisted classical capacity of noisy quantum channels, Phys. Rev. Lett. 83, 3081 (1999)

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Holevo, On entanglement-assisted classical capacity, J

A.S. Holevo, On entanglement-assisted classical capacity, J. Math. Phys. 43, 4326 (2002)

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Bell, On the Einstein Podolsky Rosen paradox, Physics Physique Fizika 1, 195 (1964)

J.S. Bell, On the Einstein Podolsky Rosen paradox, Physics Physique Fizika 1, 195 (1964)

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John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt, Proposed Experiment to Test Local Hidden-Variable Theories, Phys. Rev. Lett. 23, 880 (1969)

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Brunner, D

N. Brunner, D. Cavalcanti, S. Pironio, V . Scarani, and S. Wehner, Bell nonlocality, Rev. Mod. Phys.86, 419 (2014)

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Buhrman, R

H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, Nonloc- ality and communication complexity, Rev. Mod. Phys. 82, 665 (2010)

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Quek and P

Y. Quek and P . W. Shor, Quantum and superquantum enhancements to two-sender, two-receiver channels, Phys. Rev. A 95, 052329 (2017)

work page 2017

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J. Yun, A. Rai, and J. Bae, Nonlocal Network Coding in Interference Channels, Phys. Rev. Lett. 125, 150502 (2020)

work page 2020

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J. Yun, A. Rai, and J. Bae, Non-Local Coding in Quantum Networks : Two-Sender and Two-Receiver Scenario (in preparation), to appear on arXiv soon

work page

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Leditzky, M.A

F. Leditzky, M.A. Alhejji, J. Levin, and G. Smith, Playing games with multiple access channels, Nat. Commun. 11, 1497 (2020)

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Notzel, Entanglement enabled communication, IEEE Journal on Selected Areas in Information Theory 1.2, 401 (2020)

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