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up vote 4 down vote favorite 1 Let's say Alice wants to send Bob a $|0rangle$ with probability .5 and $|1rangle$ also with probability .5 . So after a qubit Alice prepares leaves her lab, the system could be represented by the following density matrix: $$rho = .5 |0rangle langle 0| + .5 |1rangle langle 1|= begin{bmatrix} .5 & 0 \ 0 & .5 end{bmatrix} $$ Am I right? Then, Bob would perform measurement in the standard basis. This is where I get confused. For example, he could get $|0rangle$ with probability .5 and $|1rangle$ with .5. So what is the density matrix representing the state after Bob performs his measurement in the standard basis accounting for both of his possible outcomes? quantum-information measurement cryptography density-matrix ...