Measuring Nonclassicality of Bosonic Field Quantum States via Operator Ordering Sensitivity

Area of Science:

• Quantum optics
• Quantum information theory
• Mathematical physics

Background:

• Assessing the nonclassicality of quantum states is crucial for quantum technologies.
• Existing measures have limitations in characterizing subtle quantum features.
• Understanding the Wigner function and Renyi entropy is key to quantum state analysis.

Purpose of the Study:

• Introduce a novel, distance-based measure for the nonclassicality of bosonic field states.
• Develop a method to quantify state sensitivity to operator ordering.
• Provide a precise geometric interpretation of classical states in density matrix space.

Main Methods:

• Definition of operator ordering sensitivity for quantum states.
• Utilizing Renyi entropy of quasiprobabilities.
• Analysis of Wigner function oscillations.
• Geometric mapping of states in density matrix space.

Main Results:

• A new distance-based nonclassicality measure is introduced, outperforming existing measures.
• Operator ordering sensitivity effectively quantifies state nonclassicality.
• A clear geometric distinction between classical and nonclassical states is established.
• The relationship between the new nonclassicality measure and quantum macroscopicity is clarified.

Conclusions:

• The proposed measure offers a robust and geometrically intuitive way to identify nonclassical states.
• Operator ordering sensitivity provides valuable insights into the quantum nature of states.
• This work distinguishes nonclassicality from quantum macroscopicity, highlighting distinct quantum phenomena.