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Related Concept Videos

The Uncertainty Principle04:08

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
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The de Broglie Wavelength02:32

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Updated: Jul 9, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Gap between quantum theory based on real and complex numbers is arbitrarily large.

Shubhayan Sarkar1, David Trillo2, Marc-Olivier Renou3

  • 1Faculty of Mathematics, Physics and Informatics, Uniwersytet Gdański, Wita Stwosza 57, Gdańsk, Pomeranian Voivodeship, 80-309, Poland.

Reports on Progress in Physics. Physical Society (Great Britain)
|July 7, 2026
PubMed
Summary
This summary is machine-generated.

Complex Hilbert spaces in quantum information theory predict correlations impossible in real quantum theory. This study shows the gap widens with more parties in quantum networks, highlighting limitations of real number-based quantum mechanics.

Keywords:
Bell inequalitiesQuantum networksReal and complex Hilbert spacesUnbounded gap

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Area of Science:

  • Quantum Information Science
  • Foundations of Quantum Mechanics
  • Quantum Information Theory

Background:

  • Quantum information theory utilizes complex Hilbert spaces.
  • Real quantum theory, based on real Hilbert spaces, offers an alternative framework.
  • Previous work identified discrepancies between these theories in three-party networks.

Purpose of the Study:

  • To investigate the differences between complex and real Hilbert space formalisms in larger quantum networks.
  • To construct a multipartite Bell inequality to quantify this difference.
  • To analyze the scalability of the gap and its tolerance to experimental noise.

Main Methods:

  • Studied a star network configuration with N+1 quantum parties.
  • Developed a novel multipartite Bell inequality.
  • Analyzed the asymptotic behavior of the quantum-real gap with increasing N.
  • Calculated the robustness of the observed gap against experimental errors.

Main Results:

  • A gap between quantum theory and real quantum theory was demonstrated in an N+1 party network.
  • This gap scales linearly with the number of parties (N), becoming arbitrarily large.
  • The study provides a quantitative measure of the discrepancy that grows with network complexity.
  • The tolerance of this gap to experimental errors was computed.

Conclusions:

  • Complex Hilbert space formalism is increasingly necessary for describing large quantum networks.
  • Real number-based quantum mechanics becomes inadequate for complex quantum systems as N grows.
  • The findings have implications for understanding the fundamental differences between quantum mechanics over complex and real fields.