Two-state generator extraction: property currents and a two-layer arrow of time in pre- and post-selected quantum dynamics

[2607.26999] Two-state generator extraction: property currents and a two-layer arrow of time in pre- and post-selected quantum dynamics Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2607.26999 (quant-ph) [Submitted on 29 Jul 2026 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Two-state generator extraction: property currents and a two-layer arrow of time in pre- and post-selected quantum dynamics Authors: Seiki Saito View a PDF of the paper titled Two-state generator extraction: property currents and a two-layer arrow of time in pre- and post-selected quantum dynamics, by Seiki Saito View PDF HTML (experimental) Abstract: Conditioning on both past and future assigns intermediate-time properties a causal observer does not; these time-symmetric assignments obey exact symmetry theorems and are measurable from trajectories. We use two-state generator extended dynamic mode decomposition (gEDMD): because weak values obey $dA_w/dt=i\langle[H,A]\rangle_w$ exactly, generator extraction, with an exact-derivative baseline, applies unchanged to them. First, a reflection involution on the pre-/post-selected ensemble splits every window-fitted friction uniquely as $\gamma_{fwd}=\gamma_A+\gamma_S$: $\gamma_A$, antisymmetric about the midpoint, carries the modes' boundary-condition physics; $\gamma_S$, symmetric, comes from the differencing scheme; both follow from the same data as $(\gamma_{fwd}\pm\gamma_{bwd})/2$. At a fixed inference resolution the arrow of time has two layers: the coherent-mode arrow reverses at the midpoint, the fluctuation-level one does not, $\gamma_S$ dominating $\gamma_A$ at every size and class. The difference is one of degree: $\gamma_S$ is 34 times larger there than at the mode layer, and with the exact derivative both layers reverse: immunity belongs to the inference, not the ensemble. Second, in a lattice interferometer conditioned only at its ports, the quantum Cheshire-cat structure emerges unimposed: particle and polarization obey separate continuity equations, and a local field in the polarization-carrying arm rotates that phase alone, at exactly twice the field strength, entering the generator as a rigid imaginary shift, while the particle's weak density stays invariant to machine precision. We verify the sample-level identity and the two layers from $2^8$ to $2^{20}$ dimensions: $|\gamma_A|/\gamma_S=0.09$ to $0.27$ across five classes; self-averaging makes it insensitive to class among those sharing a boundary modulation, removing the $2^{-N/2}$ overlap obstruction for $N$ qubits. Comments: 21 pages, 11 figures, 5 tables Subjects: Quantum Physics (quant-ph) ; Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2607.26999 [quant-ph] (or arXiv:2607.26999v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.26999 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Seiki Saito [ view email ] [v1] Wed, 29 Jul 2026 14:56:38 UTC (3,776 KB) [v2] Sat, 15 Aug 2026 07:06:30 UTC (3,760 KB) Full-text links: Access Paper: View a PDF of the paper titled Two-state generator extraction: property currents and a two-layer arrow of time in pre- and post-selected quantum dynamics, by Seiki Saito View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-07 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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