AMPEX Multi-Channel Recording [tech note]

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T i k)

13). The density matrix p S1 is also automatically diagonal, by the choice of representation consisting of the basis in S2 which makes p S2 diago- nal and the corresponding relative states in S 1 . & 1 j ki kj k ,-- - 1 1 ij = where l 1 i i fell. 18) * R Pld = akak'kE = Pk 6kE • Thus in the canonical representation both density matrices are diagonal and have the same elements, Pk , which give the marginal square amplitude distribution over both of the sets IQ and Ini l forming the basis of the representation.

I, A 4)(Tii, qm) - 1 [1 = Trace (p l A) , where we have defined p l in the fl el. 19) pm 2n - / (ei qn, o s ) * c i qm, os) . i It can be easily shown that here again the dependence of p l upon the choice of basis irii i in S2 , and of p 2 upon 1 eil, is only apparent. 5 A better, coordinate free representation of a mixture is in terms of the operator which the density matrix represents. For a mixture of states On (not necessarily orthogonal) with weights pn , the density operator is [O ] stands for the projection operator on O .

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