TL;DR
This paper introduces protocols to recover some information lost during unrecorded quantum measurements, where both the measured operator and outcome are unknown, highlighting differences from classical physics.
Contribution
It presents novel protocols for retrieving data from unrecorded quantum measurements, addressing a gap in understanding quantum measurement effects.
Findings
Protocols enable partial data recovery from URMs
Quantum measurements leave a detectable mark unlike classical cases
The study advances quantum measurement theory
Abstract
Projective (Von Neumann) Measurement of an operator (i.e. a dynamical variable) selected from a prescribed set of operators is termed unrecorded measurement (URM) when both the selected operator and the measurement outcome are unknown, i.e. "lost". Within classical physics a URM is completely inconsequential: the state is unaffected by measurement. Within quantum physics a measurement leaves a mark. The present study provides protocols that allow retrieval of some of the data lost in a URM.
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