Semi-quantum secure direct communication in the curved spacetime

Abstract

Cosmic string bearing energy-momentum tensor can cause spacetime bending and gravitation effect. Entanglement plays significant role in quantum communication and quantum cryptography. In this article, we examine the performance of semi-quantum secure direct communication (SQSDC) and its relation with entanglement affected by massless scalar field in the background of cosmic string spacetime. It is found that vacuum fluctuation, acceleration and nontrivial spacetime topology have profound effect on the fidelity and entanglement. Fidelity decreases fast to a fixed value and entanglement decays quickly with increasing acceleration and evolution time. When defect parameter $\nu =1$ and atom is far away from the string, the evolution model restores to that of Minkowski spacetime. When atom is very close to the string, fidelity and entanglement are similar to that of Minkowski spacetime but related to topology defect parameter. For defect parameter $\nu >1$, when acceleration is relatively small, fidelity and entanglement present oscillatory behavior for some time as atom-string distance increases. The results would shed light on quantum communication in curved spacetime.

Appendix: Field correlation function

$$\begin{aligned} G(\Delta \tau )=\frac{\nu }{8 \pi ^2 X \sqrt{\frac{1-\cosh (a \Delta \tau )}{a^2}} \sqrt{-\frac{\cosh (a \Delta \tau )}{a^2}+\frac{1}{a^2}+2 r^2} }, \end{aligned}$$

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where $\Delta \tau =\tau -\tau '$ and $\displaystyle X=\frac{2}{r^{-2 \nu } \left[ -\frac{\cosh (a \Delta \tau )}{a^2}-\sqrt{\frac{1-\cosh (a \Delta \tau )}{a^2}} \sqrt{-\frac{\cosh (a \Delta \tau )}{a^2}+\frac{1}{a^2}+2 r^2}+\frac{1}{a^2}+r^2\right] ^{\nu }+1}-1$.