Complex numbers appear throughout the mathematical formalism of quantum theory, but physicists have long debated whether they are truly essential for describing nature [1]. Could quantum phenomena instead be described using only real numbers? Over the years, two real-valued formulations of quantum theory have emerged: One preserves the standard mathematical rule for combining independent quantum systems, while the second modifies this rule [2, 3]. The first has been ruled out theoretically and experimentally, because it fails to reproduce certain “multipartite” quantum experiments [4]. The second can reproduce all predictions of standard quantum mechanics; by changing the composition rule for combined quantum systems, it ultimately requires us to rethink the basic notions of quantum information. Now Pedro Barrios Hita at the German Aerospace Center and his collaborators revisit this long-standing debate and show that it can be reframed by introducing an additional assumption—one that’s based on a physically motivated principle—about how independent quantum systems combine [5]. With this extra puzzle piece, the second approach emerges as a compelling alternative (Fig. 1).
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