What is it about?

Anyone interested in extending the results of Quantum Information Theory (QIT) to the context of Relativity must have heard of the fundamental perplexities posed by the seminal work of Peres, Scudo, and Terno in 2002. This perplexity is clarified and resolved in this paper by analyzing the mathematical anatomy of the spin reduced density matrix. This is done by exploiting the vector bundle language to describe the single-particle state space of massive spin-1/2 particle.

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Why is it important?

Any true physical theory must make sense in the context of Relativity. However, to the best of the author's knowledge, QIT has never been successfully incorporated into the relativistic context. This is because the fundamental perplexities of Relativistic Quantum Information theory (RQI) posed by the early pioneering works of the field have not seen a definitive clarification, until the publication of this paper. This paper gives a clear mathematical resolution of this problem.


Not only this paper resolves the fundamental perplexities of RQI, but also suggest a new mathematical framework to view the single-particle state spaces that is better suited for RQI investigation. The author expects that this bundle theoretic formulation of single-particle state spaces will be widely used in the future RQI research. More detailed mathematical theory has been developed and posted on arXiv. Please check "https://arxiv.org/abs/2201.04324" for a treatment of massive particles with arbitrary spin and "https://arxiv.org/abs/2201.11372" for massless particles with arbitrary helicity.

Heon Lee
Seoul National University

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This page is a summary of: Relativistic massive particle with spin-1/2: A vector bundle point of view, Journal of Mathematical Physics, January 2022, American Institute of Physics,
DOI: 10.1063/5.0064409.
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