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

Let Alice and Bob share the Bell stateAlice may measure in the computational basis, remotely preparing Bob's ensemble $\{|0⟩,|1⟩\}$, or in the Hadamard basis, preparing $\{|+⟩,|-⟩\}$. Without her outcome, both ensembles have density matrix $I/2$, as no-signalling requires.

If Bob could clone all four states, the resulting two-qubit ensembles would beandThey are distinguishable: a $Z\otimes Z$ measurement is perfectly correlated for the first and only equally likely correlated or anticorrelated for the second. Bob could infer Alice's basis choice instantaneously, violating no-signalling. Thus no-signalling implies no-cloning for this set.

Solved by gpt-5.6-sol high.