Conditional Quantum Experiments: Structure and Exponential Attraction to Permanent Memory

We study quantum instruments with finitely many outcomes on a d-dimensional system, allowing unresolved Kraus alternatives. We prove that almost surely all cluster maps of the normalized conditional evolution are reversible physical encodings of one record-dependent minimal experiment on a finite-dimensional algebra, possibly scalar. Each encoding preserves the entire logical algebra under all future observed words, whose probabilities are independent of the logical state, including its classical label. The encodings may move; the input readout need not be reversible.For every fixed finite instrument, the conditional map approaches the set of all permanent factorizations exponentially in mean diamond distance, uniformly over normalized completely positive starts under their own Born laws. Global filter stability under support inclusion holds exactly when no permanently recoverable classical bit is invisible to future records. Then stability is exponential in mean, uniformly over true states compatible with a fixed initial estimate. The obstruction admits an exact algebraic two-state test using known word maps of length at most d^2 − 1. For the identity start, the mean distance is comparable to the optimal diamond error of permanent branch approximations to the record-and-output channel preserving every record effect.Complete conditional experiments can have different sharp mean attraction rates while every finite-word effect and the full permanent locus remain fixed. We demonstrate this with an eight-dimensional one-parameter family carrying a moving, exactly recoverable qubit, in which record selection competes with residual noncommuting gauge statistics. The parameter can change the mean exponent through coherence amplitudes on rare surviving prefixes. Under the common record law, conditional products along the same record become identical across the family after a common almost-surely finite time, and the almost-sure attraction exponent is unchanged.