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Relativistic BB84, relativistic errors, and how to correct them

Marek Czachor·Marcin Wilczewski
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Abstract

The Bennett-Brassard cryptographic scheme (BB84) needs two bases, at least one of them linearly polarized. The problem is that linear polarization formulated in terms of helicities is not a relativistically covariant notion: State which is linearly polarized in one reference frame becomes depolarized in another one. We show that a relativistically moving receiver of information should define linear polarization with respect to projection of Pauli-Lubanski's vector in a principal null direction of the Lorentz transformation which defines the motion, and not with respect to the helicity basis. Such qubits do not depolarize.

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Marek Czachor, Marcin Wilczewski. 2003-04-10. Relativistic BB84, relativistic errors, and how to correct them. https://doi.org/10.1103/physreva.68.010302

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