Preserving quantum entanglement from parametric amplifications with a correlation modulation scheme

Amplification of an entangled state is a matter of great significance in quantum communication. However, any parametric amplifier (PA) will introduce added noise into the system which unavoidably degrades the entanglement or even makes it disappear. Recently, it has been experimentally demonstrated that amplification of one half of a two-mode squeezed state is possible while preserving entanglement [Phys. Rev. Lett. 103, 010501 (2009)]. However, such entanglement cannot be maintained when the strength of the amplification is large. To solve this problem, we propose a correlation modulation scheme (CMS), which fully exploits the quantum correlation between the two output states from the PA process, to suppress the added noise from the parametric amplifications. For amplifying an entangled state using a PA, we demonstrate that the CMS not only better maintains but also always preserves the entanglement whatever the strength of the PA. Such a CMS may pave the way to low-noise amplification of an entangled state.

Figure 1

Comparison between the schemes of amplifying one of two entangle states using (a) PA and (b) PACMS.

Figure 2

Entanglement enhancement from the CMS in the ideal case. For two entangled fields ${\widehat{a}}_{p1}$ and ${\widehat{a}}_{c1}$, the red asterisks (circles) show the inseparability $I_{p1c2}$ ($I_{p1c{2}^{\prime }}^{\min }$) between them versus the gain of the ${\mathrm{FWM}}_2$ when the field ${\widehat{a}}_{c1}$ is amplified by the PA (PACMS) to become ${\widehat{a}}_{c2}$ (${\widehat{a}}_{c{2}^{\prime }}$). The blue squares show the ${\xi }_{\mathrm{opt}}$ versus the gain of the ${\mathrm{FWM}}_2$ minimizing $I_{p1c{2}^{\prime }}^{\min }$. Here it is assumed that the gain of the ${\mathrm{FWM}}_1$ is two.

Figure 3

The effect of the losses on the performance of the PA and PACMS. For two entangled fields ${\widehat{a}}_{p1}$ and ${\widehat{a}}_{c1}$, the red asterisks (circles) show the inseparability $I_{p1c2}$ ($I_{p{1}^{\prime }c2}^{\min }$) between them versus the losses of the system when ${\widehat{a}}_{c1}$ is amplified by the PA (PACMS). Here it is assumed that the gains of the ${\mathrm{FWM}}_1$ and ${\mathrm{FWM}}_2$ are respectively 2 and 1.9. The blue squares show the ${\xi }_{\mathrm{opt}}$ versus the losses for minimizing $I_{p1c{2}^{\prime }}^{\min }$.

Figure 4

The schemes of amplifying both two entangled states using two PACMSs.

Figure 5

The entanglement enhancement from the CMS in the symmetrical amplification for the (a) ideal case and (b) lossy case. For two entangled fields ${\widehat{a}}_{p1}$ and ${\widehat{a}}_{c1}$ in the ideal case, the red asterisks (circles) in panel (a) show the inseparability $I_{p3c2}$ ($I_{p{3}^{\prime }c{2}^{\prime }}^{\min }$) between them versus $G_2^2$ when both of them are amplified by the PAs (PACMSs) to become ${\widehat{a}}_{p3}$ and ${\widehat{a}}_{c2}$ (${\widehat{a}}_{p{3}^{\prime }}$ and ${\widehat{a}}_{c{2}^{\prime }}$). The blue squares in panel (a) show the ${\xi }_{\mathrm{opt}}$ versus the $G_2^2$ minimizing $I_{p{3}^{\prime }c{2}^{\prime }}^{\min }$. Here it is assumed that $G_1^2=2$. For the lossy case, the red asterisks (circles) in panel (b) show the inseparability $I_{p3c2}$ ($I_{p{3}^{\prime }c{2}^{\prime }}^{\min }$) versus the losses, where it is assumed that $G_1^2=2$ and $G_2^2=1.9$. The blue squares in panel (b) show the ${\xi }_{\mathrm{opt}}$ versus the losses for minimizing $I_{p{3}^{\prime }c{2}^{\prime }}^{\min }$.