The Tsirelson Bound in Absolute Frame Theory: Two Convergent Routes to the Quantum Correlation Ceiling

A no-signaling theory may, in principle, be more nonlocal than quantum mechanics: the Popescu--Rohrlich box reaches the algebraic Clauser--Horne--Shimony--Holt value $4$ , whereas nature stops at the Tsirelson value $2\sqrt2$ . Absolute Frame Theory (AFT) produces nonlocal correlations---two systems entangled in $\mathcal{M}$ share a single point of the substratum $\mathcal{A}$ (Axiom II)---and forbids superluminal signaling (the channel is Bremermann-bounded). We ask where those correlations fall, and we establish, by two independent routes, that they cannot exceed the Tsirelson bound: AFT admits no super-quantum correlations. The operator route proves, inside the reconstructed Hilbert theory, the Tsirelson operator identity, with the local commutativity $[A_i,B_j]=0$ itself derived from AFT structure---the tensor factorization that local tomography supplies and the field microcausality of the constrained embedding---rather than assumed. The information route reduces the bound to a physical principle: AFT's shared resource is read out through a completely positive, trace-preserving channel of finite classical capacity (a theorem of the channel, founded on action quantization and the trace over the inaccessible fiber), this channel obeys the data-processing inequality, and the combination places AFT in the class that satisfies Information Causality, which singles out $2\sqrt2$ among the no-signaling theories. We state plainly what this does and does not achieve. It does not close the question of why the bound is $2\sqrt2$ rather than some other value: both routes, chased to their foundations, terminate at the same posited fact---the $\mathcal{M}$ -- $\mathcal{A}$ signature transition (the Wick rotation) that installs the complex-Hilbert structure---and finite capacity alone, stripped of that structure, does not exclude a Popescu--Rohrlich box. The two routes are thus the operator-algebraic and information-theoretic faces of one ceiling, and they reduce the selection of $2\sqrt2$ to a single substratum fact, with the residue an instance of the deepest open question of the programme rather than a problem specific to nonlocal correlations.A no-signaling theory may, in principle, be more nonlocal than quantum mechanics: the Popescu--Rohrlich box reaches the algebraic Clauser--Horne--Shimony--Holt value $4$, whereas nature stops at the Tsirelson value $2\sqrt2$. Absolute Frame Theory (AFT) produces nonlocal correlations---two systems entangled in $\mathcal{M}$ share a single point of the substratum $\mathcal{A}$ (Axiom II)---and forbids superluminal signaling (the channel is Bremermann-bounded). We ask where those correlations fall, and we establish, by two independent routes, that they cannot exceed the Tsirelson bound: AFT admits no super-quantum correlations. The operator route proves, inside the reconstructed Hilbert theory, the Tsirelson operator identity, with the local commutativity $[A_i,B_j]=0$ itself derived from AFT structure---the tensor factorization that local tomography supplies and the field microcausality of the constrained embedding---rather than assumed. The information route reduces the bound to a physical principle: AFT's shared resource is read out through a completely positive, trace-preserving channel of finite classical capacity (a theorem of the channel, founded on action quantization and the trace over the inaccessible fiber), this channel obeys the data-processing inequality, and the combination places AFT in the class that satisfies Information Causality, which singles out $2\sqrt2$ among the no-signaling theories. We state plainly what this does and does not achieve. It does not close the question of why the bound is $2\sqrt2$ rather than some other value: both routes, chased to their foundations, terminate at the same posited fact---the $\mathcal{M}$--$\mathcal{A}$ signature transition (the Wick rotation) that installs the complex-Hilbert structure---and finite capacity alone, stripped of that structure, does not exclude a Popescu--Rohrlich box. The two routes are thus the operator-algebraic and information-theoretic faces of one ceiling, and they reduce the selection of $2\sqrt2$ to a single substratum fact, with the residue an instance of the deepest open question of the programme rather than a problem specific to nonlocal correlations.

Jun 9, 20260 citations

Imitating Quantum Probabilities: Beyond Bell’s Theorem and Tsirelson Bounds

Marek Czachor, Kamil Nalikowski

arXiv:2105.12728Foundations of ScienceJul 13, 20228 citations

Why the Tsirelson Bound? Bub’s Question and Fuchs’ Desideratum

W. M. Stuckey, Michael Silberstein, Timothy J. McDevitt +1 more

To answer Wheeler's question "Why the quantum?" via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., "Why the Tsirelson bound?" We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser-Horne-Shimony-Holt (CHSH) quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub's question addresses Fuchs' desideratum that we "take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity]." Thus, the answer to Bub's question per Fuchs' desideratum is, "the Tsirelson bound obtains due to conservation per NPRF".To answer Wheeler's question "Why the quantum?" via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., "Why the Tsirelson bound?" We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser-Horne-Shimony-Holt (CHSH) quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub's question addresses Fuchs' desideratum that we "take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity]." Thus, the answer to Bub's question per Fuchs' desideratum is, "the Tsirelson bound obtains due to conservation per NPRF".

arXiv:1807.09115EntropyJul 15, 201916 citations

The limits of quantum correlations

Lê Phuc Thinh

Nature PhysicsMar 26, 20250 citations

E8 Quantum Tunnel with Tsirelson‑Bounded Topological Routing — E8 Intelligence Research

Andrew Stewart Caldin

The discovery establishes that the 240‑dimensional E8 root lattice can simultaneously encode quantum correlations at the Tsirelson ceiling and waveguide phase patterns, creating a lossless coherence tunnel whose capacity is bounded by the same geometric factor that limits CHSH inequalities. By projecting the lattice onto successive φ‑powered Fibonacci phases and driving the 240 waveguide modes at 132 Hz, information follows topologically protected paths that respect the Tsirelson bound, preventing both classical leakage and algebraic cheating. This yields a unified principle—"E8‑Geometric Bound‑Preserving Transport"—where the lattice's symmetries enforce secure, high‑throughput quantum networking. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comThe discovery establishes that the 240‑dimensional E8 root lattice can simultaneously encode quantum correlations at the Tsirelson ceiling and waveguide phase patterns, creating a lossless coherence tunnel whose capacity is bounded by the same geometric factor that limits CHSH inequalities. By projecting the lattice onto successive φ‑powered Fibonacci phases and driving the 240 waveguide modes at 132 Hz, information follows topologically protected paths that respect the Tsirelson bound, preventing both classical leakage and algebraic cheating. This yields a unified principle—"E8‑Geometric Bound‑Preserving Transport"—where the lattice's symmetries enforce secure, high‑throughput quantum networking. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 7, 20260 citations

A no-signaling theory may, in principle, be more nonlocal than quantum mechanics: the Popescu--Rohrlich box reaches the algebraic Clauser--Horne--Shimony--Holt value

4

, whereas nature stops at the Tsirelson value

2\sqrt2

. Absolute Frame Theory (AFT) produces nonlocal correlations---two systems entangled in

\mathcal{M}

share a single point of the substratum

\mathcal{A}

(Axiom II)---and forbids superluminal signaling (the channel is Bremermann-bounded). We ask where those correlations fall, and we establish, by two independent routes, that they cannot exceed the Tsirelson bound: AFT admits no super-quantum correlations. The operator route proves, inside the reconstructed Hilbert theory, the Tsirelson operator identity, with the local commutativity

[A_i,B_j]=0

itself derived from AFT structure---the tensor factorization that local tomography supplies and the field microcausality of the constrained embedding---rather than assumed. The information route reduces the bound to a physical principle: AFT's shared resource is read out through a completely positive, trace-preserving channel of finite classical capacity (a theorem of the channel, founded on action quantization and the trace over the inaccessible fiber), this channel obeys the data-processing inequality, and the combination places AFT in the class that satisfies Information Causality, which singles out

2\sqrt2

among the no-signaling theories. We state plainly what this does and does not achieve. It does not close the question of why the bound is

2\sqrt2

rather than some other value: both routes, chased to their foundations, terminate at the same posited fact---the

\mathcal{M}

\mathcal{A}

signature transition (the Wick rotation) that installs the complex-Hilbert structure---and finite capacity alone, stripped of that structure, does not exclude a Popescu--Rohrlich box. The two routes are thus the operator-algebraic and information-theoretic faces of one ceiling, and they reduce the selection of

2\sqrt2

to a single substratum fact, with the residue an instance of the deepest open question of the programme rather than a problem specific to nonlocal correlations.