Isospectral oscillators as a resource for quantum information processing

In this paper, we address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator potentials share the equally spaced energy levels of the shifted harmonic oscillator but differ significantly in that they are nonharmonic. Consequently, their ground states and thermal equilibrium states are no longer Gaussian and exhibit nonclassical properties. We quantify their non-Gaussianity and evaluate their nonclassicality using various measures, including quadrature squeezing, photon number squeezing, Wigner function negativity, and quadrature coherence scale. Additionally, we employ quantum estimation theory to identify optimal measurement strategies and establish ultimate precision bounds for inferring the deformation parameter. Our findings prove that quantum systems isospectral to the harmonic oscillator may represent promising platforms for quantum information with continuous variables. In turn, non-Gaussian and nonclassical stationary states may be obtained and these features persist at nonzero temperature.