- #1

thatboi

- 127

- 18

I am having trouble visualizing the matrix representation of the mixed density matrix from the following post (specifically from the accepted answer): https://quantumcomputing.stackexcha...ap-test-and-density-matrix-distinguishability

That is, for ##\rho_3=\frac{1}{4}\frac{1}{2^{2n}}\sum_{i,j}\left(\sum_{a,b}|a,i,j\rangle\langle b,i,j|+\sum_{a,b}(-1)^b|a,i,j\rangle\langle b,j,i|+\sum_{a,b}(-1)^a|a,j,i\rangle\langle b,i,j|+\sum_{a,b}(-1)^{a\oplus b}|a,j,i\rangle\langle b,j,i|\right)##. The user makes the statement: "We're interested by the diagonal coefficients of ##\rho_{3}## that can be written as |0,i,j⟩⟨0,i,j|. Summing them would give us the probability of measuring |0⟩. " I just wanted to confirm if ##\rho_{3}## was still an 8x8 matrix, and if so, is there an implicit assumption that the ##{i,j}## states form an orthonormal basis of their 4x4 Hilbert space?

Thanks.