Isometric properties of completely positive maps

Francesco Fidaleo, Federico Ottomano, Stefano Rossi

Uffe Haagerup, Magdalena Musat

Wolfgang Freudenberg

Markov property - recent developments on the quantum Markov property, L. Accardi and F. Fidaleo stationary quantum stochastic processes from the cohomological point-of-view, G.G. Amosov the Feller property of a class of quantum Markov semigroups II, R. Carbone and F. Fagnola recognition and teleportation, K.-H. Fichtner et al prediction errors and completely positive maps, R. Gohm multiplicative properties of double stochastic product integrals, R.L. Hudson isometric cocycles related to beam splittings, V. Liebscher multiplicativity via a hat trick, J.M. Lindsay and S.J. Wills dilation theory and continuous tensor product systems of Hilbert modules, M. Skeide quasi-free fermion planar quantum stochastic integrals, W.J. Spring and I.F. Wilde. (Part contents).

Stanley Gudder

W. A. Majewski, Tomasz I. Tylec

In their interesting paper Jiang, Luo, and Fu [Phys. Rev. A 87, 022310 (2013)] present a nice historical review of what is usually referred to as the Choi-Jamio\l{}kowski isomorphism and discuss some of its subtle properties. Our aim is to point out that there is a stronger correspondence between quantum maps and bipartite states: an isometric isomorphism between linear maps and functionals. This correspondence stems from the famous Grothendieck memoirs, and it has been a known fact at least since the 1970s. In particular, some properties studied by Jiang et al. are simple reminiscences of this more general approach. Moreover, for the sake of a complete historical review, we would like to note that the positive partial transpose criterion studied in the 1980s by Choi was, in fact, rediscovered in quantum information by Peres [Phys. Rev. Lett. 77, 1413 (1996)] and M. Horodecki et al. [Phys. Lett. A 223, 1 (1996)].

B. V. Rajarama Bhat, Robin Hillier, Nirupama Mallick +1 more