2
$\begingroup$

Given the state of a system as $\rho_s$ and that of the ancilla (pointer) as $\rho_a$, the Von-Neumann measurement involves entangling a system with ancilla and then performing a projective measurement on the ancilla. This is often represented as $$[\mathcal{I} \otimes P_i] U(\rho_s \otimes \rho_a)U^{-1} [\mathcal{I} \otimes P_i],$$ where $\mathcal{I}$ is the identity on system space, $P_i$ is the projector corresponding to $i$-th outcome, and $U$ is the combined unitary.

My question: How to choose the form of $U$?

Improve this question
$\endgroup$
5
  • $\begingroup$ are you asking given a map $\Phi$ represented as $\Phi(\rho)=\operatorname{tr}_a[U(\rho\otimes \rho_a)U^\dagger]$, how to find the unitary $U$ in this representation? $\endgroup$
    – glS ♦
    Jul 15, 2020 at 23:35
  • $\begingroup$ Actually, a simple example would be sufficient. $\endgroup$
    – Rob
    Jul 16, 2020 at 10:48
  • $\begingroup$ a simple example of what? $\endgroup$
    – glS ♦
    Jul 16, 2020 at 11:28
  • $\begingroup$ An example of U, that would lead to a valid measurement. $\endgroup$
    – Rob
    Jul 16, 2020 at 13:39
  • $\begingroup$ I am asking the following: Given the combined state $\rho_s \otimes \rho_a$, give an example (or a general form) of $U$, such that the quantity I wrote in my question, represents a valid measurement. $\endgroup$
    – Rob
    Jul 16, 2020 at 16:44

0

Reset to default

Your Answer

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