H. Araki, "On a Characterization of the State Space of Quantum Mechanics," Comm. Math. Phys. 75, 1--24 (1980); W. K. Wootters, "Local Accessibility of Quantum Information," in Complexity, Entropy and the Physics of Information, edited by W. H. Zurek (Addison-Wesley, Redwood City, CA, 1990), p. 29--46.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....satisfying the (DADB ) tr = f(E i , F j ) 57) Such an operator always exists. Consequently we have, # i # j tr . 58) For complex Hilbert spaces , the uniqueness of follows because the set F j forms a complete basis for the Hermitian operators on . [71] For real Hilbert spaces, however, the analog of the Hermitian operators are the symmetric operators. The dimensionality of the space of symmetric operators on a real Hilbert space D(D 1) rather than the D it is for the complex case. This means that in the steps above only 1 DADB (DA ....

H. Araki, "On a Characterization of the State Space of Quantum Mechanics," Comm. Math. Phys. 75, 1--24 (1980); W. K. Wootters, "Local Accessibility of Quantum Information," in Complexity, Entropy and the Physics of Information, edited by W. H. Zurek (Addison-Wesley, Redwood City, CA, 1990), p. 29--46.

....in Sec. IV fails for real Hilbert spaces, but it does not establish that the theorem itself fails. The main point of this discussion is that it draws attention to the crucial di erence between real Hilbert space and complex Hilbertspace quantum mechanics a fact emphasized previously by Araki [26] and Wootters [27] To show that the theorem fails, we need a counterexample. One such example is provided by the N system state 1 1 ; 5.2) 1 2 (I 2 ) and = 1 2 (I 2 ) 5.3) and where 2 was de ned in Eq. 3.2) In complex Hilbert space quantum mechanics, ....

H. Araki, \On a Characterization of the State Space of Quantum Mechanics," Comm. Math. Phys. 75, 1 (1980).

....series of events, open system algorithms must necessarily be used 9 in particular the most interesting infinite dimensional case. 10 e.g. Phase space can be considered in some cases as a submanifold of the state space, the embedding being implemented via coherent states. 11 See e.g. Ref. [9] 12 Notice however the discussion in Piron, Giovannini, Reusse [10, 11, 12] and also the discussion of probabilistic interpretation of the nonlinear Schrodinger equation: Ref. 13, 14] 4 . Kahler manifolds naturally embedded into projective Hilbert space of quantum states . for p=q=2 ....

H. Araki, "On a characterization of the state space of quantum mechanics, " Commun.math. Phys, 75 (1980) 1--24

....CP (n Gamma1) On the level of convex structure the difference between the classical and quantum state space is well understood. The classical one is a Choquet simplex and different axiomatizations of the quantum one are available in the literature, the reader may be referred to the works [4, 5], for example. Our main concern here is the possible Riemannian structure in the quantum case. Before turning to that subject, we review briefly the classical case, that is, the Riemannian structure on the space of measures. From the viewpoint of information geometry, the spherical representation ....

H. Araki, On the characterization of the state space in quantum mechanics, Commun. Math. Phys. 75(1980), 1--25

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H. Araki, "On a Characterization of the State Space of Quantum Mechanics," Comm. Math. Phys. 75, 1--24 (

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