Meta-Quantum Metrology via Universal Rough Operator Algebra (UROA): Subsuming SQL and Decoherence through Topological 8D Projection

Abstract

The fundamental precision limits in quantum sensing—dictated by the Standard Quantum Limit (SQL), multi-parameter incompatibility [2], and Markovian decoherence [1]—are deductively subsumed and algebraically elevated using the Seonggil Theory of Composite Torsion (STCT) and UROA. By redefining parameter estimation processes as trajectories within an 8-Dimensional Non-commutative Tensor Space, classical noise boundaries are topologically shielded. This framework rigorously yields robust Super-Heisenberg scaling and enables simultaneous optimal multi-parameter observability.