Schrödinger cat states in continuous variable non-Gaussian networks

Teleportation with a cubic phase gate

“…This entails ambiguity in the Eq. ( 16) and the emergence of a state like the Schrödinger's cat state [27], which in our case leads to a rapid increase in the error variances.…”

“…In addition, we had to resort to approximations that limit the applicability of our result. It is also worth mentioning that Heisenberg's approach may give incorrect results when describing transformations over non-Gaussian resources [27]. Bearing in mind all of the above, we repeat the above procedure but use the language of wave functions to describe it without resorting to any approximations.…”

Quantum statistics of Schrödinger cat states prepared by logical gate with non-Gaussian resource state

“…It was shown recently [18], that continuous-variable measurement-induced two-node logical gate is able to prepare Schrödinger cat-like quantum superpositions, if Gaussian (e. g. squeezed) resource state of an ancillary oscillator is substituted with non-Gaussian one. This was demonstrated for the cubic phase state used as a resource.…”

“…An important distinction between the gate [18] and the non-Gaussian circuits mentioned above is that the Schrödinger cat state emerges when the ancillary oscillator measurement is compatible not with one, but with two different values of the target oscillator physical variables. This feature does not appear in Gaussian quantum networks and, given that a non-Gaussian resource state is used, needs the measurement which is consistent with this criterion.…”

“…Our analysis is based on the exact form of the output state [18]. At the same time, the gate operation may be illustrated in terms of an approximate visual representation of the step-by-step quadrature amplitudes transformations in the scheme if one considers these transformations in a semiclassical manner.…”