Nonlocal advantage of quantum imaginarity in Schwarzchild spacetime

Abstract

Black hole spacetimes provide a natural setting for quantum systems in curved spacetime, where effects such as Hawking radiation arise from event horizons. In this work, we investigate the impact of the Hawking effect on quantum imaginarity in Schwarzschild spacetime, focusing on nonlocal advantage of quantum imaginarity (NAQI) and assisted imaginarity distillation. For NAQI, it is significantly affected by Hawking radiation, exhibiting a pronounced difference between physically accessible and inaccessible regions. It is suppressed in the physically accessible region with increasing Hawking temperature and may vanish, while remaining absent in the physically inaccessible region across the parameter regime. For assisted imaginarity distillation, the Hawking effect modifies the assisted fidelity in a state-dependent manner. In the physically accessible region, the fidelity generally decreases with increasing temperature, indicating reduced distillation capability, whereas the physically inaccessible region exhibits the opposite monotonic trend, indicating enhanced distillation capability. These results highlight distinct operational behaviors of physically accessible and inaccessible regions under relativistic effects, providing insight into quantum imaginarity in curved spacetime.

Figures (6)

• Figure 1: NAQI gap $\Delta_{l_1}$ for $\rho^{AB_{\text{out}}}$ and $\rho^{AB_{\text{in}}}$. Panels $(a)$ and $(b)$ correspond to $\rho^{AB_{\text{out}}}$, while panels (c) and (d) correspond to $\rho^{AB_{\text{in}}}$. Panels $(a)$ and $(c)$ show $\Delta_{l_1}$ as a function of $\delta$ for fixed $p=0,0.2,0.3,0.5$, with $\delta\in[0,\pi/4)$. Panels $(b)$ and $(d)$ display $\Delta_{l_1}$ as a function of $p$ for fixed $\delta=0,0.4,0.6,0.7$, with $p\in[0,1]$. The horizontal gray solid line indicates $\Delta_{l_1}=0$. The black dots mark the critical values of $\delta$ at which $\Delta_{l_1}$ becomes zero.
• Figure 2: NAQI gap $\Delta_{rel}$ for $\rho^{AB_{\text{out}}}$ and $\rho^{AB_{\text{in}}}$. Panels $(a)$ and $(b)$ correspond to $\rho^{AB_{\text{out}}}$, while panels (c) and (d) correspond to $\rho^{AB_{\text{in}}}$. Panels (a) and (c) show $\Delta_{rel}$ as a function of $\delta$ for fixed $p=0,0.2,0.3,0.5$, with $\delta\in[0,\pi/4)$. Panels (b) and (d) show $\Delta_{rel}$ as a function of $p$ for fixed $\delta=0,0.4,0.6,0.7$, with $p\in[0,1]$. The horizontal gray line indicates $\Delta_{rel}=0$. The black dots mark the critical values of $\delta$ at which $\Delta_{rel}$ reaches zero.
• Figure 3: NAQI gap $\Delta_{l_1}$ for $\rho_{W}^{AB_{\mathrm{out}}}$ and $\rho_{W}^{AB_{\mathrm{in}}}$. Panels (a) and (c) show $\Delta_{l_1}$ as a function of $\delta$ for fixed $p=0,0.7,0.8,1.0$, with $\delta\in[0,\pi/4)$. Panels (b) and (d) show $\Delta_{l_1}$ as a function of $p$ for fixed $\delta=0,0.5,0.7,0.75$, with $p\in[0,1]$. The horizontal gray line indicates $\Delta_{l_1}=0$, and the black dots mark the corresponding critical values of $\delta$ at which $\Delta_{l_1}$ reaches zero.
• Figure 4: NAQI gap $\Delta_{rel}$ for $\rho_{W}^{AB_{\mathrm{out}}}$ and $\rho_{W}^{AB_{\mathrm{in}}}$. Panels (a) and (c) show $\Delta_{rel}$ as a function of $\delta$ for fixed $p=0,0.8,0.9,1.0$, with $\delta\in[0,\pi/4)$. Panels (b) and (d) show $\Delta_{rel}$ as a function of $p$ for fixed $\delta=0,0.5,0.6,0.7$, with $p\in[0,1]$. The horizontal gray line indicates $\Delta_{rel}=0$, and the black dots mark the corresponding critical values of $\delta$ at which $\Delta_{rel}$ reaches zero.
• Figure 5: Assisted imaginarity fidelity $F_{d}(\rho^{AB_{\text{out}}})$ and $F_{d}(\rho^{AB_{\text{in}}})$. Panels $(a)$ and $(b)$ show the fidelity as a function of $\delta$ for $p=0,0.2,0.3,0.5$. Panels $(c)$ and $(d)$ present the corresponding quantities over the parameter space $(\delta, p)$.