We present a general algorithm for finding all classes of pure multiparticle states equivalent under stochastic local operations and classical communication (SLOCC). We parametrize all SLOCC classes by the critical sets of the total variance function. Our method works for arbitrary systems of distinguishable and indistinguishable particles. We also show how to calculate the Morse indices of critical points which have the interpretation of the number of independent nonlocal perturbations increasing the variance and hence entanglement of a state. We illustrate our method by two examples.We present a general algorithm for finding all classes of pure multiparticle states equivalent under stochastic local operations and classical communication (SLOCC). We parametrize all SLOCC classes by the critical sets of the total variance function. Our method works for arbitrary systems of distinguishable and indistinguishable particles. We also show how to calculate the Morse indices of critical points which have the interpretation of the number of independent nonlocal perturbations increasing the variance and hence entanglement of a state. We illustrate our method by two examples.

arXiv:1208.0557Physical Review AOct 18, 201245 citations

Stochastic diagonalization

Hans A. De Raedt

Physics ReportsAug 1, 199352 citations

Gravitational Record Formation - A Stochastic Collapse Model Driven by Teleparallel Torsion

SIKX HILTON

We propose a stochastic modification of nonrelativistic quantum dynamics in which state-vector reduction is triggered by a gravitational distinguishability functional, identified here as the weak-field limit of the Torsion scalar in Einstein’s Teleparallel Equivalent of General Relativity (TEGR). By grounding the collapse mechanism in spacetime torsion rather than curvature, we resolve the fundamental ambiguity of gravitational energy localization found in standard General Relativity. The model is designed so that individual experimental runs admit nonlinear, finite-time localization dynamics driven by accumulated torsion distinguishability, while the ensemble state admits a linear evolution compatible with a no-signaling constraint. Two empirical parameters are introduced: a record-capacity scale $S^*$ (representing a critical torsion threshold) and a spatial resolution scale $r_c$ . We summarize the dynamical postulates, clarify their domain of validity, and outline falsifiable signatures in high-mass matter-wave interferometry, establishing this framework as a consistent low-energy limit of a torsion-based relativistic collapse theory.We propose a stochastic modification of nonrelativistic quantum dynamics in which state-vector reduction is triggered by a gravitational distinguishability functional, identified here as the weak-field limit of the Torsion scalar in Einstein’s Teleparallel Equivalent of General Relativity (TEGR). By grounding the collapse mechanism in spacetime torsion rather than curvature, we resolve the fundamental ambiguity of gravitational energy localization found in standard General Relativity. The model is designed so that individual experimental runs admit nonlinear, finite-time localization dynamics driven by accumulated torsion distinguishability, while the ensemble state admits a linear evolution compatible with a no-signaling constraint. Two empirical parameters are introduced: a record-capacity scale $S^*$ (representing a critical torsion threshold) and a spatial resolution scale $r_c$. We summarize the dynamical postulates, clarify their domain of validity, and outline falsifiable signatures in high-mass matter-wave interferometry, establishing this framework as a consistent low-energy limit of a torsion-based relativistic collapse theory.

Jan 13, 20260 citations

S^*

(representing a critical torsion threshold) and a spatial resolution scale

r_c

. We summarize the dynamical postulates, clarify their domain of validity, and outline falsifiable signatures in high-mass matter-wave interferometry, establishing this framework as a consistent low-energy limit of a torsion-based relativistic collapse theory.