The (Fisher) information matrix (I2p) for a p×p density matrix (ρ) is taken to be the (2p2+p)‐dimensional information matrix of a 2p‐variate real normal distribution with an apriori zero mean vector and a covariance matrix (Σ2p), the two diagonal blocks of which are formed from the symmetric (real) component of ρ, and the two off‐diagonal blocks from the skew‐symmetric (imaginary) part of ρ. The inverse square root ‖nI2p−1/2 (where n is the number of observations) serves as a unitary invariant prior distribution over (the precision matrices) Σ2p−1 and ‖nI2p1/2 over Σ2p—and consequently over the p×p (mixed and pure) density matrices. The availability of these priors should facilitate the process of state determination. An uncertainty principle for the estimation of ρ is formulated. The determinant of Σ2p proves for integral p≥1 to equal (2p‖ρ‖)2.

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