Combinatorial optical complex wavelet-fractional Fourier transform

Area of Science:

• Quantum Optics
• Quantum Information Theory
• Wavelet Transforms

Background:

• Quantum optical states are fundamental to quantum information processing.
• Analyzing and identifying these states is crucial for advancements in quantum technologies.
• Existing methods may have limitations in characterizing complex quantum states.

Purpose of the Study:

• To introduce a novel mathematical transform for quantum optics.
• To develop a new tool for analyzing and identifying quantum optical states.
• To explore the application of this transform to specific quantum states.

Main Methods:

• Utilizing the technique of integration within ordered product of operators.
• Formulating the combinatorial optical complex wavelet-fractional Fourier transform.
• Deducing the normally ordered form of the unitary operator for the transform.

Main Results:

• The unitary operator for the new transform was successfully derived.
• The normally ordered form of the operator was deduced.
• The transform was applied to two-mode vacuum and number states, demonstrating its utility.

Conclusions:

• The combinatorial optical complex wavelet-fractional Fourier transform is a viable new tool in quantum optics.
• This transform can effectively analyze and identify various quantum optical states.
• The method offers potential for further research in quantum state characterization.