Quantum mechanics based on real numbers: A consistent description

• URL: http://arxiv.org/abs/2503.17307v1
• Date: Fri, 21 Mar 2025 16:56:30 GMT
• Title: Quantum mechanics based on real numbers: A consistent description
• Authors: Pedro Barrios Hita, Anton Trushechkin, Hermann Kampermann, Michael Epping, Dagmar Bruß,
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Complex numbers play a crucial role in quantum mechanics. However, their necessity remains debated: whether they are fundamental or merely convenient. Recently, it was claimed that quantum mechanics based on real numbers can be experimentally falsified in the sense that any real-number formulation of quantum mechanics either becomes inconsistent with multipartite experiments or violates certain postulates. In this article we show that a physically motivated postulate about composite quantum systems allows to construct quantum mechanics based on real numbers that reproduces predictions for all multipartite quantum experiments. Thus, we argue that real-valued quantum mechanics cannot be falsified, and therefore the use of complex numbers is a matter of convenience.

Related papers

• Are Molecules Magical? Non-Stabilizerness in Molecular Bonding [50.24983453990065]
  Isolated atoms as well as molecules at equilibrium are presumed to be simple from the point of view of quantum computational complexity. We show that the process of chemical bond formation is accompanied by a marked increase in the quantum complexity of the electronic ground state.
  arXiv  Detail & Related papers  (2025-04-09T08:14:27Z)
• Quantum theory does not need complex numbers [0.0]
  A decisive argument was presented asserting that quantum theory needs complex numbers. We show that a formulation of quantum theory based solely on real numbers is possible. We conclude that complex numbers are a mere convenience in quantum theory.
  arXiv  Detail & Related papers  (2025-04-03T17:53:19Z)
• Invariance under quantum permutations rules out parastatistics [0.0]
  We argue that quantum systems should not only preserve their local state under permutations, but also the quantum information that they carry about other systems.<n>For both, we show that the respective principle is fulfilled if and only if the particle is a Boson or Fermion.
  arXiv  Detail & Related papers  (2025-02-24T19:01:11Z)
• A computational test of quantum contextuality, and even simpler proofs of quantumness [43.25018099464869]
  We show that an arbitrary contextuality game can be compiled into an operational "test of contextuality" involving a single quantum device. Our work can be seen as using cryptography to enforce spatial separation within subsystems of a single quantum device.
  arXiv  Detail & Related papers  (2024-05-10T19:30:23Z)
• 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)
• Is there evidence for exponential quantum advantage in quantum chemistry? [45.33336180477751]
  The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. It may be prudent to assume exponential speedups are not generically available for this problem.
  arXiv  Detail & Related papers  (2022-08-03T16:33:57Z)
• Testing the necessity of complex numbers in traditional quantum theory with quantum computers [0.0]
  A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers.<n>To motivate the experiment, we present a basic construction for real-valued quantum theory.<n>The results obtained with quantum computers are consistent with published experiments.
  arXiv  Detail & Related papers  (2022-05-03T01:06:16Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• 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)
• 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)
• Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks [48.7576911714538]
  Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
  arXiv  Detail & Related papers  (2020-12-11T12:55:17Z)
• 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)

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.