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Contents of PMS, Vol. 33, Fasc. 2,
pages 191 - 199
 

SOME DECOMPOSITIONS OF MATRIX VARIANCES

Zoltán Léka
Dénes Petz

Abstract: When D is a density matrix and A ,A 1 2 are self-adjoint operators, then the standard variance is a 2 ×2 matrix:

V arD(A1,A2)i,j := TrDAiAj - (TrDAi)(TrDAj ) (1 ≤ i,j ≤ 2).
The main result in this work is that there are projections Pk such that ∑ D = kλkPk with 0 < λk and ∑ kλk = 1 and ∑ V arD(A1,A2) = k λkVarPk(A1,A2) . In a previous paper only the A1 = A2 case was included and the relevance is motivated by the paper [8].

2000 AMS Mathematics Subject Classification: Primary: 62J10; Secondary: 62F30.

Keywords and phrases: Density matrix, variance, covariance, decomposition, projections.Marekċ Częysóołwski

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