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Implementing Bell causality in quantum sequential growth

Ritesh Srivastava1,2 and Sumati Surya2

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Phys. Rev. D 114, 086007 – Published 7 October, 2026

DOI: https://doi.org/10.1103/thx5-dknv

Abstract

We explore different implementations of the quantum Bell causality (QBC) condition in the quantum sequential growth (QSG) dynamics of causal set quantum gravity, for noncommuting transition operators. Assuming a nonsingular dynamics we show that for the two most natural choices of operator orderings for the QBC, the transition operator algebra A reduces to a commutative one. As a third choice, we take the operator ordering to depend on the size of the precursor set. We find several new commutation relations which further constrain A but do not imply commutativity. On the other hand, if any of the generators of the “antichain subalgebra” Q belongs to its center, then this implies commutativity of A. The complexity of the algebra prevents us from obtaining a general form for the transition operators, which hinders computability. In an attempt to construct the simplest nontrivial d=2 representation of A, we find that a Pauli matrix representation of the generators of Q leads to inconsistencies. Our work can be viewed as a first step toward finding a noncommutative realization of QSG.

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Phys. Rev. D 114, 086007– Published 7 October, 2026
  • Received 26 March 2026
  • Accepted 11 August 2026
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