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Measurement Contextuality and Planck's Constant.

Lucas Kocia1, Peter Love2

  • 1Department of Physics, Tufts University, Medford, Massachusetts 02155, U.S.A. and National Institute of Standards and Technology, Gaithersburg, MD, 20899.

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|June 29, 2026
PubMed
Summary
This summary is machine-generated.

Contextuality in quantum computation is linked to Planck's constant orders. Higher-order terms in the Wigner-Weyl-Moyal formalism explain why qubits show state-independent contextuality, while odd-dimensional qudits exhibit state-dependent contextuality.

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Area of Science:

  • Quantum Information Theory
  • Quantum Computation
  • Mathematical Physics

Background:

  • Contextuality is a key resource for universal quantum computation.
  • Non-contextual quantum mechanics can often be simulated efficiently on classical computers.
  • Orders of Planck's constant (ℏ) can delineate the classical-quantum boundary, with higher orders representing quantum corrections.

Purpose of the Study:

  • To investigate the relationship between contextuality and orders of Planck's constant (ℏ) within the Wigner-Weyl-Moyal (WWM) formalism.
  • To explain the differing contextuality behaviors observed in qubits versus odd-dimensional qudits.
  • To establish a formal link between contextuality as a quantum resource and the ℏ expansion.

Main Methods:

  • Formulation of contextual measurements in finite-dimensional systems using the Wigner-Weyl-Moyal (WWM) formalism.
  • Analysis of expectation values and their dependence on orders of ℏ.
  • Comparison of WWM formulations for qubit and odd-dimensional qudit observables.

Main Results:

  • Contextual measurements require higher-than-order ℏ⁰ terms in the WWM formalism to violate classical bounds.
  • Contextuality as a resource is directly related to orders of ℏ within the WWM formalism.
  • Qubit Pauli observables lack ℏ⁰ contributions, leading to state-independent contextuality, while odd-dimensional qudit observables generally possess non-zero ℏ⁰ terms, enabling state-dependent contextuality.

Conclusions:

  • The order of Planck's constant (ℏ) in WWM formulations provides a fundamental explanation for the observed differences in contextuality between qubits and odd-dimensional qudits.
  • Contextuality's role as a quantum computational resource is intrinsically tied to the non-classical contributions (higher orders of ℏ) in quantum mechanical descriptions.
  • Odd-dimensional qudits exhibiting measurement contextuality necessitate an order ℏ¹ contribution in their expectation values with specific observables.