Ex4 9

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 4.9}$

Design a measurement on a $3$-qubit system that distinguishes between states in which all bit values are equal and those in which they are not, and gives no other information. Write all operators in bra/ket notation.

page revision: 0, last edited: 18 Nov 2012 18:22

In order to do this, we just need to assign two distinct eigenvalues to the two distinct eigenspaces we are trying to measure (all bit values are equal & all bit values are not equal). The solution below uses 2 for the eigenvalue for the eigenspace where all bit values are equal and 6 for the eigenvalue for the eigenspace where all bit values are not equal.

(1)ReplyOptionsIt could be argued that the simple

(1)which represents the comparison outcome as $1$ for true and $0$ for false is a better choice of eigenvalues, in line with the remark on p.56.

ReplyOptions