Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 10D / c / Solution

No. In quantum dense coding, Alice's four encodings produce four different joint Bell states, but the qubit she transmits has reduced statein every case. Charlie intercepts only that qubit, so every measurement he can perform has the same probability distribution for messages $00,01,10,11$. He gains no information about the two-bit string.