Density matriX Fact. A matrix p is a density matrix of some mixed quantum state iff p is positive semi-definite(psd) Tr(p=1 Recall Amatrix M is psd if all its eigenvalues are nonnegative. Equivalently, if (v Mv)20,Vv The trace of a matrix M is Tr(M)=2i MiDensity matrix • Fact. A matrix 𝜌 is a density matrix of some mixed quantum state iff – 𝜌 is positive semi-definite (psd) – Tr 𝜌 = 1. • Recall: – A matrix 𝑀 is psd if all its eigenvalues are nonnegative. Equivalently, if 𝑣 𝑀 𝑣 ≥ 0, ∀𝑣. – The trace of a matrix 𝑀 is Tr 𝑀 = σ𝑖 𝑀𝑖𝑖