Questions tagged [textbook-and-exercises]

Applies to questions of primarily educational value - styled in the format similar to that found in textbook exercises. This tag should be applied to questions that are (1) stated in the form of an exercise and (2) at the level of basic quantum information textbooks.

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Representing a von Neumann measurement as $[\mathcal{I} \otimes P_i] U(\rho_s \otimes \rho_a)U^{-1} [\mathcal{I} \otimes P_i]$, how do we choose $U$?

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 ...
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Step-by-step passages in calculation

I would like to better understand some passages in a paper (Appendix A): Properties of Tensor Product Bilinearity: $A\otimes(B+ C) = A \otimes B + A \otimes C $ Mixed-product property: $(A\otimes B)(...
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How do you decompose an arbitrary quantum state into its corresponding projection subspaces such that their direct sum is the quantum state?

I understand that every Hilbert space $H$ can be decomposed into two mutually orthogonal subspaces $H_1$ and $H_2$ whose direct sum is $H$. Therefore, every vector $v\in H$ can be decomposed into $...