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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Quantum mechanics: why complex Hilbert space?

G Cassinelli1, P Lahti2

  • 1Department of Physics, University of Genoa and INFN Genoa Unit, Genoa, Italy.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|October 4, 2017
PubMed
Summary
This summary is machine-generated.

This study reconstructs quantum mechanics axiomatically using the statistical duality of states and effects. It leverages Solér

Keywords:
axiomscompound systemsstatistical dualitysymmetrytheorem of Solér

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Area of Science:

  • Quantum mechanics
  • Foundational questions in physics

Background:

  • Quantum mechanics requires axiomatic reconstruction for deeper understanding.
  • Statistical duality of states and effects is a key concept.
  • The 'Second quantum revolution' prompts foundational inquiries.

Purpose of the Study:

  • To propose an axiomatic framework for quantum mechanics.
  • To explore the role of statistical duality in this reconstruction.
  • To justify the use of the complex field in quantum theory.

Main Methods:

  • Utilizing Solér's theorem within the axiomatic approach.
  • Incorporating the principle of symmetry.
  • Analyzing arguments for the complex field's necessity.

Main Results:

  • A novel axiomatic reconstruction of quantum mechanics is presented.
  • The statistical duality of states and effects is shown to be fundamental.
  • Arguments supporting the complex field are discussed.

Conclusions:

  • The proposed axiomatic program offers a new perspective on quantum foundations.
  • Symmetry and statistical duality are crucial for rebuilding quantum theory.
  • The complex field is a natural choice within this framework.