Finite-classical-record quantum state reconstruction: one-shot bounds and acquisition limits
Abstract
Abstract We study the one-shot reconstruction of a quantum state when a single copy of the source is measured, the outcome is stored in a classical record of fixed finite dimension, and a state is prepared at the destination from the record. This acquisition-limited problem is distinguished from a visible benchmark in which the source label is available to the encoder. For a finite ensemble we derive finite-record bounds on the visible distortion in terms of the cumulative prior mass covered by the record and the optimal discrimination probability, identify the regimes in which they are exact, and solve the two-state visible problem at every record dimension. For pure-state ensembles, exact acquisition-limited reconstruction is possible if and only if the states are perfectly distinguishable, so nonorthogonal targets retain a positive error at every record dimension. For two equiprobable nonorthogonal pure states we derive the optimal trace-distance distortion within the reflection-symmetric two-outcome class in closed variational form and find that unrestricted numerical optimization with up to six outcomes attains the same value; the resulting symmetric value lies strictly below the guess-and-prepare, unambiguous-discrimination, fidelity-optimal, and Haar-random strategies and is realized by one classical bit and one feed-forward rotation. Every classical-record reconstruction is shown to be entanglement breaking, with a quantitative bound on the loss of entanglement with…
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