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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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