Ex10 30

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 10.30}$

a) Describe a strategy for determining which sequence was sent in the game of Section 10.3 if both qubits are received. More specifically, you receive a sequence of pairs of qubits. Either all pairs are randomly chosen from $\{\ket{00}, \ket{11} \}$ or all pairs are in the state $\frac{1}{\sqrt 2}(\ket{00} + \ket{11})$. Describe a strategy for determining which wequence was sent.

b) For each sequence, write down the density operator representing that sequence.