Relativistic Motion Generates Quantum Gates and Entanglement Resonances

We show that the relativistic motion of a quantum system can be used to generate quantum gates. The nonuniform acceleration of a cavity is used to generate well-known two-mode quantum gates in continuous variables. Observable amounts of entanglement between the cavity modes are produced through resonances that appear by repeating periodically any trajectory.

Figure 1

The relativistic motion of the cavity is used to produce a two-mode squeezing gate. The input (red) and output (blue) states are Gaussian states. The nonuniform motion of the cavity produces two-mode squeezing. The procedure to enhance the effect is illustrated in the magnified green oval: by repeating $N$ times an arbitrary trajectory characterized by a total proper time $T$ (represented by the single box in the smaller oval at the top), the degree of squeezing is linearly increased.

Figure 2

The correction to the symplectic eigenvalue ${\tilde{\nu }}_N^{(1)}$ after $N=5$ segment repetitions as a function of the proper time of acceleration $\tau$ and the time of coasting $t$. We considered a cavity length of $L=1$, massless modes $k=1$ and $k^{\prime }=2$, and accelerations $a=a^{\prime }={10}^{-4}$.