The success of quantum mechanics is due to the discovery that nature is described in infinite dimension Hilbert spaces, so that it is desirable to demonstrate the quantum teleportation process in a certain infinite dimensional Hilbert space. We describe the teleportation process in an infinite dimensional Hilbert space by giving simple examples.

Journal of Mathematical PhysicsOct 1, 20056 citations

Correlations in infinite systems

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arXiv:1711.07323 · The European Physical Journal B

Bath-induced correlations in an infinite-dimensional Hilbert space

Marco Nizama, Manuel O. Cáceres

Published Sep 1, 2017• 2 citations

arXiv HTML PDF

DOI: 10.1140/epjb/e2017-80231-4

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T>0

the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We found a time-scale that characterizes the time when the bath-induced correlation is maximum before being wipe out by dissipation (purity, spatial, and mirror correlations are studied). We introduce a Wigner function associated to the Wannier lattice where the dissipative quantum walks move. Thus we discuss the peculiarities of the scenario of enlarging the lattice to the semi-integers in order to fulfilll all the fundamental properties of the Wigner function. We have supported the quantum character of the correlations by analyzing the negativity of the Wigner function.