A general-purpose path-recording oracle is defined that perfectly simulates random elements of any closed subgroup of U(N) by storing t input-output pairs whose updates are governed by the commutant of the group's tensor-power representation.
The compressed oracle is a worthy (multiplicative) adversary
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Quantum Lazy Sampling and Path Recording for Any Group
A general-purpose path-recording oracle is defined that perfectly simulates random elements of any closed subgroup of U(N) by storing t input-output pairs whose updates are governed by the commutant of the group's tensor-power representation.