Superpositions of Binomial States and Schrödinger Cats

Abstract

We introduce quantum superpositions of binomial states ∣Ψ〉_s), such that¹

$$ \left| {{\Psi _s}} \right\rangle = N\sum\limits_{n = 0}^M {[1 + ( - {1^n}{e^{i\phi }}]} B_n^M\left| n \right\rangle , $$

((1))

where $N = {\left[ {2\left( {1 + \cos \phi \Sigma _{n = 0}^m{{\left( { - 1} \right)}^n}{{\left| {B_n^M} \right|}^2}} \right)} \right]^{ - 1/2}}$ is the normalization factor, and ∅ a relative phase connected to the generation process.