Ex11 19

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 11.19}$

Let $[[n, k, d]]$ be any non-degenerate code. Such a code can correct $t = \lfloor\frac{d-1}{2}\rfloor$ errors. Show that tracing any codeword over any $n-t$ qubits results in the totally mixed state $\rho = \frac{1}{2^t} I$ on the remaining $t$ qubits. Thus all codewords are highly entangled states.