P. M. Alberti, "A note on the transition probability over C -algebras," Lett. Math. Phys., vol. 7, pp. 25--32, 1983. Home/Search Document Not in Database Summary Related Articles Check |
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On Quantum Coding for Ensembles of Mixed States - Barnum, Caves, Fuchs, Jozsa, .. (2000) (Correct)
....subspace D. Then F (ae; ae 0 ) is less than the sum of the d largest eigenvalues of ae, which we write as 1 Gamma j. Proof of Lemma A1: We use the fact that F (ae; ae 0 ) inf trace aeA trace ae 0 A Gamma1 ; 24) where the infimum is over all strictly positive operators A [28]. Choose A = I on D, fflI on D (for any ffl 0) Then trace ae 0 A Gamma1 = 1 ; and trace aeA = trace aeD ffl trace aeD 1 Gamma j ffl trace aeD 1 Gamma j : Hence F (ae; ae 0 ) trace aeA trace ae 0 A Gamma1 1 Gamma j ; as required. To set the stage ....
P. M. Alberti, "A note on the transition probability over C -algebras," Lett. Math. Phys., vol. 7, pp. 25--32, 1983.
Spheres and Hemispheres as Quantum State Spaces - Uhlmann (1994) (Correct)
.... definition (13) we compare it with the transition probability in the state space of unital algebras, 19] 36] The rather different definitions in these references turned out to coincide for unital C algebras, 33] 11] For two states, 1 ; 2 of a unital C algebra A one knows [3] p( 1 ; 2 ) inf 1 (A) 2 (A Gamma1 ) A 0 A; A Gamma1 2 A (14) A similar relation is true with (13) At first, a power A (k) of an observable A = A x; is defined by the substitutions x 7 x, 7 ( k , and 7 ( k . Here k is a natural number and, if and both are ....
P. M. Alberti, A Note on Transition Probability over C -Algebras, Lett. Math. Phys. 7 (1983) 25
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