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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 15E / d / Solution

The overlap is
(79)
The Helstrom-Holevo bound for two equiprobable pure states gives
(80)
The Breidbart basis is the eigenbasis of the difference of the two weighted state projectors, so its decision rule is precisely the Helstrom measurement and attains this bound.
Solved by gpt-5.6-sol high.

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