2025/10/21 by A. G. Kolpakov, Kolpakov, Alexander
Computer Science · Physics and Astronomy · #E.4 #F.1 #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2510.18186
openalex publication_date 2025/10/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We introduce a frequency-tunable, two-dimensional non-Abelian control of operation order constructed from the reduced Burau representation of the braid group B3, specialised at t=eiω and unitarized by Squier's Hermitian form. Coupled to two non-commuting qubit unitaries A, B, the resulting switch admits a closed expression for the single-shot Helstrom success probability and a fixed-order ceiling pfixed, defining the fixed-order ceiling pfixed^* and the witness gaps Δ\rm sw(ω)=pswitch(ω)-pfixed^* and Δ\rm test(ω)=ptest(ω)-pfixed^*. The non-Abelian mixers can either enhance or suppress the bare switch advantage, which we quantify by the interference contrast Δ\rm int(ω):=Δ\rm test(ω)-Δ\rm sw(ω)=p\rm test(ω)-p\rm switch(ω). Across the Squier positivity region, Δ\rm int(ω) takes both positive (constructive) and negative (destructive) values, a hallmark of matrix-valued (non-Abelian) order control, while Δ\rm sw(ω)>0 certifies algebraic causal non-separability. Numerical simulations confirm both enhancement and suppression regimes, establishing a minimal B3 braid control that reproduces the characteristic interference pattern expected from a Gedankenexperiment in anyonic statistics.