Teleportation with a Uniformly Accelerated Partner

In this work, we give a description of the process of teleportation between Alice in an inertial frame, and Rob who is in uniform acceleration with respect to Alice. The fidelity of the teleportation is reduced due to Davies-Unruh radiation in Rob’s frame. In so far as teleportation is a measure of entanglement, our results suggest that quantum entanglement is degraded in noninertial frames.

Figure 1

Minkowski diagram for the case of Alice stationary while Rob (gray hyperbola) undergoes constant acceleration. Alice and Rob share an entangled Bell state at the event $P$ and can communicate as long as Alice stays within Rob’s past ${\mathcal{H}}_{-}$ and future ${\mathcal{H}}_{+}$ particle horizons, corresponding to Rob’s proper times $\tau =-\infty$ and $\tau =+\infty$, respectively.

Figure 2

Cavities $A$ (Alice, Minkowski), $R$ (Rob, Rindler), and $C$ (client cavity, Minkowski). (a) For $\tau <0$, Rob’s cavity moving with constant acceleration $a$ in the negative $z$ direction. (b) At $\tau =0$, $A$ and $R$ overlap and a four-photon entangled state is shared between the two cavities. (c) At some time $\tau >0$, Alice makes a Bell measurement with the unknown state in $C$ and her half of the Bell state in $A$. $R$ moves with constant acceleration in positive $z$ direction.

Figure 3

Rob’s entropy information gain (in bits) $\Delta S_{\mathrm{g}\mathrm{a}\mathrm{i}\mathrm{n}}=S_{\mathrm{p}\mathrm{r}\mathrm{e}}-S_{\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{t}}$ upon receiving Alice’s measurement results: numerical (solid) and $\Delta S_{\mathrm{g}\mathrm{a}\mathrm{i}\mathrm{n}}^{n=2}$ (dashed) for a five-state, $n=\{1,2\}$ excitation model using the $\{|0,1{⟩}_I,|1,0{⟩}_I\}$ and $\{|0,2{⟩}_I,|1,1{⟩}_I,|0,2{⟩}_I\}$ sector from Rob’s postmeasurement state, with $x_{ij}=y_{ij}=1/\sqrt{2}$.