{
  "id": 6404372,
  "title": "Real-number quantum theory can be more wrong than you thought",
  "url": "https://urgent.news/2026/09/09/real-number-quantum-theory-can-be-more-wrong-than-you-thought",
  "topic": "science",
  "section": "Science",
  "published": "2026-09-09T09:29:06.000Z",
  "source": {
    "name": "Physics World",
    "slug": "physics-world",
    "url": "https://physicsworld.com/a/real-number-quantum-theory-can-be-more-wrong-than-you-thought/"
  },
  "original_language": "en",
  "account": "In the 16th century, imaginary numbers first emerged as a mathematical invention, primarily used to solve equations that real numbers couldn't. Initially, many viewed these numbers as convenient tricks rather than a fundamental aspect of reality. Despite the controversy surrounding them at the time, imaginary numbers are now essential tools in physics and mathematics, including quantum mechanics. Quantum mechanics often employs complex numbers, which combine both real and imaginary components. In many simple quantum systems, using complex numbers might just be a mathematical convenience. Researchers are debating whether complex numbers are merely a convenience, a trick, or an essential requirement for understanding complex quantum systems, and if they are necessary, how far they extend.\n\nTo address this question, researchers from France, Poland, and Spain have conducted a study focusing on the composition postulate, a fundamental principle in quantum mechanics that outlines how quantum systems are combined mathematically. The team examined a star-shaped quantum network, in which multiple parties each receive a segment of a quantum system, with a central party, named \"Eve,\" receiving information from independent sources. Each party conducts simple measurements, while Eve carries out a measurement with numerous possible outcomes. The researchers employed a specially designed conditional Bell test, a method for comparing classical physics with quantum mechanics and evaluating correlations predicted by various theories.\n\nThe researchers compared two theories: standard quantum theory, which uses complex numbers, and a variant of the theory that relies solely on real numbers. They discovered that the ratio between the predictions of these two theories grows proportionally to N-1, where N represents the size of the quantum network. This means that as the network grows larger, real-number quantum theory becomes progressively worse at replicating the results of the standard complex-number quantum theory. Consequently, the study provides a definitive answer to the question of whether complex numbers are necessary in sufficiently large quantum networks. When the composition postulate is upheld, complex numbers are physically required, offering an advantage that can become arbitrarily large.",
  "summary": "Imaginary numbers first appeared in the 16th century as a mathematical invention, introduced to solve equations that real numbers could not. As the name implies, many treated them as kind of trick to get results, rather than an underlying truth about the nature of reality. Although highly controversial at the time, these numbers are now ubiquitous […] The post Real-number quantum theory can be…",
  "key_points": [],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}