Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 10D / a

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Solution

The no-signalling theorem states that any trace-preserving quantum operation performed locally by Bob leaves Alice's reduced density matrix unchanged when Bob's outcome is not communicated:

Tr_{B} [(I \otimes E_{B}) (ρ_{A B})] = Tr_{B} ρ_{A B} .

Thus Bob's choice cannot change the statistics of any measurement made by Alice.

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