2025/04/03 by Timothee Hoffreumon, Timothée Hoffreumon, Mischa P. Woods +2 · 5 voices · 6 citations
Physics and Astronomy · #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.48550/arxiv.2504.02808
openalex publication_date 2025/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum theory was radically different from the theories of nature which came before it. One key difference was its use of complex numbers. This opened a longstanding debate over whether quantum theory fundamentally requires complex numbers -- or if their use is merely a convenient choice. Until recently, this question was considered open. However, in a 2021 Nature article, a decisive argument was presented asserting that quantum theory needs complex numbers since real-number quantum theory is inconsistent with the postulates of quantum theory. In this work, we show that this conclusion was premature, and in actual fact, a real-number quantum theory is consistent with the postulates of quantum theory. Our theory retains key features such as representation locality (i.e. local physical operations are represented by local changes to the states). A direct consequence of our results is that quantum theory based on real or complex numbers are experimentally indistinguishable.