Results 1 to 10 of about 2,396 (56)

From the Jordan Product to Riemannian Geometries on Classical and Quantum States. [PDF]

Entropy (Basel), 2020
The Jordan product on the self-adjoint part of a finite-dimensional $C^{*}$-algebra $\mathscr{A}$ is shown to give rise to Riemannian metric tensors on suitable manifolds of states on $\mathscr{A}$, and the covariant derivative, the geodesics, the ...
Ciaglia FM, Jost J, Schwachhöfer L.
europepmc   +4 more sources

Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C*-algebras [PDF]

, 2014
We show that the existence of a surjective isometry (which is merely a distance preserving map) between the unitary groups of unital C*-algebras implies the existence of a Jordan *-isomorphism between the algebras.
Andruchow, Conway, Corach, Ellis, Fleming, Fleming, Hatori, Hatori, Hatori, Hatori, Hatori, Hu, Kadison, Kadison, Kadison, Kubo, Lajos Molnár, Mankiewicz, Miura, Molnár, Osamu Hatori, Sakai, Sakai, Sourour, Thompson, Šemrl   +25 more
core   +1 more source

The Two-fold Role of Observables in Classical and Quantum Kinematics [PDF]

, 2017
Observables have a dual nature in both classical and quantum kinematics: they are at the same time \emph{quantities}, allowing to separate states by means of their numerical values, and \emph{generators of transformations}, establishing relations between
Zalamea, Federico
core   +2 more sources

Poisson spaces with a transition probability [PDF]

, 1996
The common structure of the space of pure states $P$ of a classical or a quantum mechanical system is that of a Poisson space with a transition probability.
Landsman, N. P.
core   +6 more sources

Reduction of Lie-Jordan Banach algebras and quantum states

, 2012
A theory of reduction of Lie-Jordan Banach algebras with respect to either a Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared with the standard reduction of C*-algebras of observables of a quantum system in the presence of ...
A Ibort, Dirac P A M, Emch G G, F Falceto, G Marmo, Giachetta G, Grabowski J, Haag R, Ibort A, Kadison R V, L Ferro   +10 more
core   +1 more source

Local triple derivations on real C*-algebras and JB*-triples [PDF]

, 2013
We study when a local triple derivation on a real JB*-triple is a triple derivation. We find an example of a (real linear) local triple derivation on a rank-one Cartan factor of type I which is not a triple derivation.
Alexis Molino, Antonio, Francisco J. Fernández-polo, M. Peralta   +3 more
core  

Contractive projections and operator spaces

, 2002
Parallel to the study of finite dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces H_n^k,0< k < n+1, generalizing the row and column Hilbert spaces
Neal, Matthew, Russo, Bernard
core   +1 more source

Quantum Tomography twenty years later

, 2015
A sample of some relevant developments that have taken place during the last twenty years in classical and quantum tomography are displayed. We will present a general conceptual framework that provides a simple unifying mathematical picture for all of ...
Asorey, M., Ibort, A., Marmo, G., Ventriglia, F.   +3 more
core   +1 more source

Positive contractive projections on noncommutative $\mathrm{L}^p$-spaces

, 2020
In this paper, we prove the first theorems on contractive projections on general noncommutative $\mathrm{L}^p$-spaces associated with non-type I von Neumann algebras where $1 < p < \infty$.
Arhancet, Cédric
core  

States and synaptic algebras

, 2016
Different versions of the notion of a state have been formulated for various so-called quantum structures. In this paper, we investigate the interplay among states on synaptic algebras and on its sub-structures.
Foulis, David J., Jencova, Anna, Pulmannova, Sylvia   +2 more
core   +1 more source