Matrix inverse and its properties The matrix M = ∑piσi ⊗ σi∗ where pi is probability and σi is Pauli matrix has an inverse(its determinant det M is not equal to 0), i.e. the following three conditions must hold simultaneously, (i)q1:= p0 + p1 − p2 − p3 6= 0, (ii) q2 := p0 − p1 + p2 − p3 6= 0, (iii) q3 := p0 − p1 − p2 + p3 6= 0 How are q1, q2, q3 derived?
2026-03-26 06:14:09.1774505649
Conditions for inverse of a matrix
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The matrix you are interested in is $$ M=\begin{pmatrix} p_0+p_3 & 0 & 0 & p_1+p_2\\ 0 & p_0-p_3 & p_1 - p_2 & 0\\ 0 & p_1 - p_2 & p_0-p_3 & 0\\ p_1+p_2 & 0 & 0 & p_0+p_3 \end{pmatrix}. $$ Compute the determinant. When is it equal to zero?