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Effects, Instruments, and Access-Specified Recovery in Relational Quantum Mechanics

Liao, Qingxiang
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philosophy
Effect-based formulations of relational quantum mechanics provide a natural representation of calibrated sharp and unsharp outcome content, but associating effects with Kraus operations does not settle what an effect itself represents. This paper identifies two underdetermination gaps. First, identical calibrated effects fix every labelled first-outcome probability but need not yield the same conditional operational realisation. Effect-equivalent instruments can have orthogonal conditional outputs and maximally distinguishable flagged channels. Second, an identical immediate instrument need not yield the same later access-specified recovery. With the immediate instrument and a perfect source record fixed, alternative storage processes yield either perfect designated-memory recovery or the prior baseline. A finite-dimensional model separates source encoding, intervening dynamics, subsystem access, and the decoder class. The analysis uses established measurement theory and one-shot state discrimination; its contribution is to organise those tools into two controlled non-implications and a common inference constraint. Effects remain adequate for implementation-invariant calibrated event-type content, while token-level conditional operational realisation and later recovery require separate premises. The paper neither rejects effects nor proposes a new measurement formalism, information measure, or interpretation of quantum mechanics.
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