Uniqueness of Noncontextual Models for Stabilizer Subtheories.

Area of Science:

• Quantum Information Theory
• Foundations of Quantum Mechanics
• Quantum Computation

Background:

• Stabilizer subtheories are crucial components of quantum information processing.
• Understanding the (non)classicality of these subtheories is key to developing quantum technologies.
• Quasiprobability representations offer insights into quantum correlations and contextuality.

Purpose of the Study:

• To fully characterize the (non)classicality of all stabilizer subtheories.
• To identify unique representations and their implications for noncontextuality.
• To explore the role of generalized contextuality in quantum computation.

Main Methods:

• Characterization of stabilizer subtheories using quasiprobability representations.
• Proof of the existence and uniqueness of Gross's discrete Wigner function in odd dimensions.
• Demonstration of the nonexistence of such representations in even dimensions.

Main Results:

• A unique nonnegative, diagram-preserving quasiprobability representation (Gross's discrete Wigner function) exists for stabilizer subtheories in odd dimensions.
• This representation is equivalent to Spekkens' toy theory, identifying it as the unique noncontextual ontological model.
• Generalized contextuality is shown to be a necessary resource for universal quantum computation in the state injection model.
• Stabilizer subtheories are proven to be contextual in all even dimensions due to the nonexistence of such representations.

Conclusions:

• Noncontextuality principles can uniquely identify classical realist interpretations within specific quantum settings.
• The findings explain the utility of Gross's representation and highlight the resourcefulness of generalized contextuality.
• The dimensionality of the system critically determines the contextuality of stabilizer subtheories.