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Quantum information processing in the neighborhood of a black hole

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Abstract

Using an imperfectly prepared state, we show that in relativistic settings, the evolution of a massive spin-1/2 particle violates many standard assumptions made in quantum information theory, including complete positivity. Unlike other recent endeavors in relativistic quantum information, we are able to quantify and maximize how much information can be transferred through such a quantum process by calculating its scope. We show that, surprisingly, relativistic noise can increase the amount of information that can be transferred, and in fact, even if the initial state is arbitrarily close to the completely mixed state, information can still be transferred perfectly. Additionally, we explore the relativistic effects of velocity and gravity on quantum information processing, and we briefly discuss how quantum computation is affected by general relativity. In particular, we show that the large Wigner rotation caused by a black hole as described in the Schwarzchild metric can greatly increase the informatic content of a qubit.

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Acknowledgements

We are grateful to K. Martin and D. Terno for their helpful discussions during the preparation of this manuscript. In particular, we are thankful for the insightful discussions with Keye Martin about radiative processes of charged particles in the accretion disk of a black hole. We are also grateful to the organizers of the 17th conference on Unconventional Computation and Natural Computation, Serghei Verlan and Susan Stepney, where a truncated version of this paper was presented. We received great feedback that helped shape this extended version. In particular, we would like to thank Susan Stepney for displaying interest in the far-fetched idea of relativistic steganographic quantum communication. That discussion helped inspire the section on kinematic noise.

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  1. The Naval Research Laboratory, Washington, DC, 20375, USA

    Tanner Crowder & Marco Lanzagorta

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  1. Tanner Crowder
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  2. Marco Lanzagorta
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Correspondence to Tanner Crowder.

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Crowder, T., Lanzagorta, M. Quantum information processing in the neighborhood of a black hole. Nat Comput 18, 549–561 (2019). https://doi.org/10.1007/s11047-019-09737-7

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