In this work we study different types of coherent and squeezed states for the Charlier, Kravchuk and Meixner oscillators. We calculate the average values of different observables corresponding to the coherent states. We found that the coherent and squeezed states of the Kravchuk oscillator are unstable. There are also coherent and squeezed states that are similar to the coherent and squeezed states of the harmonic oscillator. We have introduced a discrete variable model for the biophoton coherent radiation, and the coherent thermal and squeezed thermal states.
We show how discrete squeezed states in an
N2-dimensional phase space can be properly constructed out of the finite-dimensional context. Such discrete extensions are then applied to the framework of quantum tomography and quantum information theory with the aim of establishing an initial study on the interference effects between discrete variables in a finite phase space. Moreover, the interpretation of the squeezing effects is seen to be direct in the present approach, and has some potential applications in different branches of physics.
Quantum mechanics imposes ``monogamy'' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully ``promiscuous,'' i.e., simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of
N-mode $(N\ensuremath{\geqslant}4)$ Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of individual qubits. Such a finding is of importance for the quantification, understanding, and potential exploitation of shared quantum correlations in continuous variable systems. We discuss how promiscuity gradually arises when considering simple families of discrete variable states, with increasing Hilbert space dimension towards the continuous variable limit. Such models are somehow analogous to Gaussian states with asymptotically diverging, but finite, squeezing. In this respect, we find that non-Gaussian states (which in general are more entangled than Gaussian states) exhibit also the interesting feature that their entanglement is more shareable: in the non-Gaussian multipartite arena, unlimited promiscuity can be already achieved among three entangled parties, while this is impossible for Gaussian, even infinitely squeezed states.