Dynamical Casimir effect in quantum-information processing

We demonstrate, in the regime of ultrastrong matter-field coupling, the strong connection between the dynamical Casimir effect (DCE) and the performance of quantum-information protocols. Our results are illustrated by means of a realistic quantum communication channel and show that the DCE is a fundamental limit for quantum computation and communication and that novel schemes are required to implement ultrafast and reliable quantum gates. Strategies to partially counteract the DCE are also discussed.

Figure 1

Schematic drawing of the quantum protocol discussed in the text. The coupling between the qubit ${\mathsf{Q}}_i$ and the cavity $\mathsf{C}$ is modulated by the function $f_i\left(t\right)$. By initially preparing ${\mathsf{Q}}_1$ in the state $\rho$, ${\mathsf{Q}}_2$ is found in the state ${\rho }^{\prime }$ at the end of the protocol.

Figure 2

Coherent information $I_c\left({\rho }_u\right)$ (full curve, left axis), single-shot quantum capacity $Q_1$ (gray circles, left axis), and mean photon number $\langle n\rangle$ (right axis) as a function of the qubit-field coupling strength $g$. The mean photon number is shown for the pure DCE (dotted curve) and at the end of the quantum communication protocol (dashed curve). The time intervals of the protocol are $T_1=T_2=\pi /2g$ and $T_c=0$. As we point out in the text, with a very good approximation $Q_1\simeq I_c\left({\rho }_u\right)$. Here and in the following figures the coherent information in computed for the maximally mixed input state ${\rho }_u$.

Figure 3

Coherent information $I_c\left({\rho }_u\right)$ (main figure) and transmission rate $R$ (inset) as a function of the coupling strength $g$, for the transmission window discussed in the text, with $\xi =0$ (full curve), $\xi =0.2$ (dashed curve), and $\xi =0.5$ (dotted curve). As in Fig. 2, $T_1=T_2=\pi /2g$ and $T_c=0$.

Figure 4

Coherent information $I_c\left({\rho }_u\right)$ (main figure) and transmission rate $R$ (inset) as a function of the coupling strength $g$, for the standard protocol (full curve) and after optimization over the times $T_1,T_2$, and $T_c$.

Figure 5

Nonzero parameters of the Fano representation of the quantum channel $\mathcal{E}$, as a function of the coupling strength $g$, for $T_1=T_2=\pi /2g$, $T_c=0$, and sudden switch on and off of the couplings.