Quantum speedup from nonclassical polarization

Abstract

We develop a framework for identifying nonclassical speedups in systems with polarization, likewise spin degrees of freedom. By confining the dynamics to the manifold of angular momentum coherent states, which act as the classical reference in this case, we compute the speed limit that bounds the rate of change of the state achievable without generating quantum coherence. A comparison with the unrestricted quantum speed limit enables the quantitative identification of speedups arising from polarization nonclassicality. We apply this framework to the cross-Kerr interaction, demonstrating a persistent speedup scaling as $\mathcal{O}(\sqrt{N})$ with the photon number $N$. The results establish polarization nonclassicality as a genuine dynamical resource, linking quantum coherence to quantum-enhanced evolution speeds in nonlinear photonic systems.

Figures (3)

• Figure 1: Time evolution of the normalized Stokes vectors for the unrestricted (turquoise) and classical (purple) case for $\varepsilon=0.05$ and the initial conditions $\alpha_{+}=0.95$ and $\alpha_{-}=0.29+0.12i$. Note that the polar angle of the evolution on the Poincaré sphere is constant, and we thus only only show the $r_x$-$r_y$ plane.
• Figure 2: Hilbert-Schmidt distance $D_{\text{HS}}$ between classical and quantum evolutions as a function of time $t$ and coupling strength $\varepsilon$ for $|\alpha_+|^2=0.9$ and $N=10$.
• Figure 3: Plot of the quantum speedup via the ratio $Q(N)$ of the unrestricted and the classical QSLs. Since $Q(N)>1$, the nonclassical speedup of cross-Kerr processes is certified. The plot exhibits an advantage of even photon numbers for small photon numbers $N$ and scales as $\mathcal{O}(N^{1/2})$ for larger $N$.