0
$\begingroup$

Consider a transformation $U_a=\sigma_z^{a_1}\otimes...\sigma_z^{a_N}$, here $\sigma_z$ is the Pauli Z operator. $a_i$ is either 0 or 1. Hence, $\sigma_z^{0}=I$ where $I$ is identity matrix.

If I use polarization of light as a qubit, can I implement this transformation using just polarizers? Please help me justify it.

$\endgroup$
2
  • 1
    $\begingroup$ what do you mean by "please help me justify it"? Where did you encounter this statement? $\endgroup$
    – glS
    Commented Jul 9, 2021 at 11:30
  • $\begingroup$ Do you know about wave plates? $\endgroup$ Commented Jul 9, 2021 at 13:56

1 Answer 1

1
$\begingroup$

With polarizers you can implement projections. The Pauli Z oerator has an eigenvalue $-1$, so no, you cannot implement $U_a$ with only polarizers.

$\endgroup$
2
  • $\begingroup$ Why does an eigenvalue -1 create a problem? $\endgroup$ Commented Jul 9, 2021 at 14:13
  • 1
    $\begingroup$ @ChetanWaghela A product of projectors will not have a negative eigenvalue, so this is one way to see why you will need some more building blocks to implement $U_a$ $\endgroup$
    – M. Stern
    Commented Jul 9, 2021 at 19:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.