quant-ph — Quantum Physics

Quantum-Information Probes of Collapse Dynamics in Causal Fermion Systems

Contributed by Benjamin Kaminsky

Finster, Kleiner, and Paganini derived from causal fermion systems (CFS) a nonrelativistic effective collapse model whose statistical operator obeys, to leading order, a Kossakowski--Lindblad equation. In the factorized regime of that derivation, the dissipator is built from purely spatial operators $N_{k,a}$ with positive rates fixed by microscopic time-nonlocal kernels. We translate this CFS-specific generator into quantities accessible to coherent quantum processors. The resulting CFS Dirichlet form obeys an exact purity-loss identity under arbitrary Hamiltonian control, and its null algebra is the commutant of the $*$-algebra generated by the projected $N_{k,a}$. For joint eigenbranches we obtain an exact distinguishability functional controlling exponential coherence loss and a lower bound on channel distance from ideal unitary evolution. In an $n$-qubit dephasing sector, the projected kernels generate a positive-semidefinite covariance matrix $C$, with GHZ visibility $\exp[-2T\bm{1}^{\mathsf T}C\bm{1}]$. We prove that uniformly summable finite-range correlations yield at most $O(n)$ GHZ decay, whereas $O(n^2)$ scaling requires a collective non-summable component. Single- and two-qubit cat coherences reconstruct $C$, giving a covariance-spectroscopy protocol, while Knill--Laflamme conditions characterize first-order correctability of the projected CFS error algebra. We also derive an explicit compatibility inequality between macroscopic state reduction and long coherent computation and show why absence of probe heating does not imply absence of coherence signatures. The results do not exclude CFS: its covariance strength, $\ellmin$, and hardware projection remain underdetermined. They instead identify the microscopic input required for a genuine no-go theorem and establish scalable quantum processors as direct probes of the CFS collapse sector.