109 research outputs found
Conditional SIC-POVMs
In this paper, we examine a generalization of the symmetric informationally complete POVMs. SIC-POVMs are the optimal measurements for full quantum tomography, but if some parameters of the density matrix are known, then the optimal SIC POVM should be orthogonal to a subspace. This gives the concept of the conditional SIC-POVM. The existence is not known in general, but we give a result in the special case when the diagonal is known of the density matrix. © 1963-2012 IEEE
Complementarity and the algebraic structure of 4-level quantum systems
The history of complementary observables and mutual unbiased bases is
reviewed. A characterization is given in terms of conditional entropy of
subalgebras. The concept of complementarity is extended to non-commutative
subalgebras. Complementary decompositions of a 4-level quantum system are
described and a characterization of the Bell basis is obtained.Comment: 19 page
Means of positive matrices
Means of positive numbers are well-know but the theory of matrix means
due to Kubo and Ando is less known. The lecture gives a short introduction
to means, the emphasis is on matrices. It is shown that any two-variablemean
of matrices can be extended to more variables. The n-variable-mean
M
) is deïŹned by a symmetrization procedure when the ntuple
(A
n
(A
1
; A
1
2
; : : : ; A
; A
2
n
) is ordered, it is continuous and monotone in each variable.
The geometric mean of matrices has a nice interpretation in terms of
an information geometry and the ordering of the n-tuple is not necessary for
the deïŹnition. It is conjectured that this strong condition might be weakened
for some other means, too.
Key Words: operator means, information geometry, logarithmic mean, geometric
mean, positive matrices.
AMS ClassiïŹcation Number: 47A64 (15A48, 47A63
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