Quantum theory does not need complex numbers

• URL: http://arxiv.org/abs/2504.02808v2
• Date: Thu, 09 Oct 2025 17:57:43 GMT
• Title: Quantum theory does not need complex numbers
• Authors: Timothee Hoffreumon, Mischa P. Woods,
• Abstract summary: We show that a real-number quantum theory is consistent with the postulates of quantum theory.<n>A direct consequence of our results is that quantum theory based on real or complex numbers are experimentally indistinguishable.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Locality Implies Complex Numbers in Quantum Mechanics [0.0]
  We show that a real-number quantum theory, compatible with the independent source assumption, requires the inclusion of a nonlocal map. If the independent source assumption holds, complex-number quantum theory is equivalent to a real-number quantum theory with hidden nonlocal degrees of freedom.
  arXiv  Detail & Related papers  (2025-04-10T14:47:00Z)
• Quantum mechanics based on real numbers: A consistent description [0.0]
  We show that a physically motivated postulate about composite quantum systems allows to construct quantum mechanics based on real numbers.<n>We argue that real-valued quantum mechanics cannot be falsified, and therefore the use of complex numbers is a matter of convenience.
  arXiv  Detail & Related papers  (2025-03-21T16:56:30Z)
• Minimal Equational Theories for Quantum Circuits [44.99833362998488]
  We show that any true equation on quantum circuits can be derived from simple rules. One of our main contributions is to prove the minimality of the equational theory.
  arXiv  Detail & Related papers  (2023-11-13T17:11:25Z)
• Quantum Circuit Completeness: Extensions and Simplifications [44.99833362998488]
  The first complete equational theory for quantum circuits has only recently been introduced. We simplify the equational theory by proving that several rules can be derived from the remaining ones. The complete equational theory can be extended to quantum circuits with ancillae or qubit discarding.
  arXiv  Detail & Related papers  (2023-03-06T13:31:27Z)
• Is there a finite complete set of monotones in any quantum resource theory? [39.58317527488534]
  We show that there does not exist a finite set of resource monotones which completely determines all state transformations. We show that totally ordered theories allow for free transformations between all pure states.
  arXiv  Detail & Related papers  (2022-12-05T18:28:36Z)
• Real quantum operations and state transformations [44.99833362998488]
  Resource theory of imaginarity provides a useful framework to understand the role of complex numbers. In the first part of this article, we study the properties of real'' (quantum) operations in single-party and bipartite settings. In the second part of this article, we focus on the problem of single copy state transformation via real quantum operations.
  arXiv  Detail & Related papers  (2022-10-28T01:08:16Z)
• No-signalling constrains quantum computation with indefinite causal structure [45.279573215172285]
  We develop a formalism for quantum computation with indefinite causal structures. We characterize the computational structure of higher order quantum maps. We prove that these rules, which have a computational and information-theoretic nature, are determined by the more physical notion of the signalling relations between the quantum systems.
  arXiv  Detail & Related papers  (2022-02-21T13:43:50Z)
• Testing real quantum theory in an optical quantum network [1.6720048283946962]
  We show that tests in the spirit of a Bell inequality can reveal quantum predictions in entanglement swapping scenarios. We disproving real quantum theory as a universal physical theory.
  arXiv  Detail & Related papers  (2021-11-30T05:09:36Z)
• Ruling out real-valued standard formalism of quantum theory [19.015836913247288]
  A quantum game has been developed to distinguish standard quantum theory from its real-number analog. We experimentally implement the quantum game based on entanglement swapping with a state-of-the-art fidelity of 0.952(1). Our results disprove the real-number formulation and establish the indispensable role of complex numbers in the standard quantum theory.
  arXiv  Detail & Related papers  (2021-03-15T03:56:13Z)
• Resource theory of imaginarity: Quantification and state conversion [48.7576911714538]
  Resource theory of imaginarity has been introduced, allowing for a systematic study of complex numbers in quantum mechanics and quantum information theory. We investigate imaginarity quantification, focusing on the geometric imaginarity and the robustness of imaginarity, and apply these tools to the state conversion problem in imaginarity theory. Our study reveals the significance of complex numbers in quantum physics, and proves that imaginarity is a resource in optical experiments.
  arXiv  Detail & Related papers  (2021-03-02T15:30:27Z)
• Quantum theory based on real numbers can be experimentally falsified [0.0]
  We show that real and complex quantum theory make different predictions in network scenarios comprising independent states and measurements. This allows us to devise a Bell-like experiment whose successful realization would disprove real quantum theory.
  arXiv  Detail & Related papers  (2021-01-26T15:25:39Z)
• Operational Resource Theory of Imaginarity [48.7576911714538]
  We show that quantum states are easier to create and manipulate if they only have real elements. As an application, we show that imaginarity plays a crucial role for state discrimination.
  arXiv  Detail & Related papers  (2020-07-29T14:03:38Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.