Catability as a metric for evaluating superposed coherent states

Abstract

Superposed coherent states are central to quantum technologies, yet their reliable identification remains a challenge, especially in noisy or resource-constrained settings. We introduce a novel, directly measurable criterion for detecting cat-like features in quantum states, rooted in the concept of nonlinear squeezing. This approach bypasses the need for full state tomography and reveals structure where fidelity fails. The numerical results confirm its robustness under loss and its potential for experimental implementation. The method naturally generalizes to more exotic superpositions, including multiheaded cat states.

Figures (2)

• Figure 1: Comparison of cat states subjected to different degrees of pure loss. The red curves represent the optimal values of the normalized infidelity \ref{['eq:normed_infi']}, while the blue curves correspond to the optimal values of catability \ref{['eq:catability']}, all relative to the transmissivity $\eta$ of the loss channel. The left column shows results for odd-parity cat states and their approximations, with (a) squeezed single photon (${r \approx -5}$ dB), and cats with amplitudes ${\alpha^{-} \in \{ 0.5, 1.5, 2.5 \}}$ in panels (b) through (d), respectively. The results for even-parity states are presented in the right column, with (e) squeezed superposition of $\ket{0}$ and $\ket{2}$ (${\omega = 0.618}$, ${r \approx -5}$ dB), and cats with amplitudes ${\alpha^{+} \in \{ 0.5, 1.5, 2.5 \}}$ within panels (f) through (h).
• Figure 2: Simulated direct measurement of the operator \ref{['eq:measurable_<O>_pn']} for an odd-parity cat state with amplitude $\alpha = 2$ subjected to different levels of amplitude loss. Colors indicate $0\%$ (red), $10\%$ (green), $20\%$ (blue), and $30\%$ (yellow) loss. (a) The dashed line indicates the mean value of the operator with respect to the number of performed measurements. The shaded regions represent uncertainty up to one standard deviation. (b) The standard deviation depends on the number of measurements.