Cubic nonlinear squeezing and its decoherence

Abstract

Squeezed states of the harmonic oscillator are a common resource in applications of quantum technology. If the noise is suppressed in a nonlinear combination of quadrature operators, the quantum states are non-Gaussian and we refer to the noise reduction as nonlinear squeezing. Non-Gaussian aspects of quantum states are often those most vulnerable to decoherence due to imperfections appearing in realistic experimental implementations. We analyze the behavior of quantum states with cubic nonlinear squeezing under loss and dephasing. The properties of nonlinear squeezed states depend on their initial parameters that can be optimized and adjusted to achieve the maximal robustness for the potential applications.

Taming numerical errors in simulations of continuous variable non-Gaussian state preparation

“…In a more realistic analysis of the preparation circuit it would be straightforward to include the propagation losses affecting the mode carrying the resulting state. This form of decoherence can be accounted for by modifying the squeezing strength of the non-linearly squeezed state [60]. Consequently we do not consider this additional attenuation since it does not influence the fundamental properties of these non-Gaussian states.…”

“…Nonlinear squeezing was originally introduced [44] as a measure quantifying the quality of approximate cubic states suitable for optical measurement-induced quantum gates [34,44]. It has been shown to apply to higher ordered phase squeezing gates as well [34] and was recently discussed in detail [60]. Originally [44] presented an implementation of a deterministic, measurement induced cubic interaction gate.…”

“…We adapted the concept of nonlinear squeezing discussed in [44] to fit our simulation. In contrast, we employ a modified nonlinear quadrature Ŷ = 𝜇 X + 𝜅𝜇 −2 P2 with 𝜅 ≡ √ 2 −1 as per [60]. This corresponds to the exp(𝚤𝜈 P3 ) cubic unitary rather than the usual exp(𝚤𝜈 X3 ).…”

“…We use the variance 𝑉 ( Ŷ , ρ) = ( Ŷ − Ŷ ρ ) 2 ρ of the Ŷ quadrature to measure the nonlinear squeezing within arbitrary states ρ. The actual figure of merit is minimized over the parameter 𝜇 to eliminate effects of Gaussian squeezing [44,60]. We therefore base our analysis on the minimized quantity 𝑊 ( ρ) min 𝜇 𝑉 ( Ŷ , ρ).…”