Quantum Digitization of Electromagnetic Field States: A Computational Tool for Investigating Encoding-Dependent Quantum Information Measures

Abstract

We present a comprehensive computational tool for investigating the quantum digitization problem: how to represent continuous electromagnetic field states as discrete qubit registers. The encoding of quantum field states into finite qubit systems is a fundamental challenge in quantum information theory, with significant implications for quantum computing, communication, and metrology. We introduce two Mathematica-based analysis functions, QubitInfoPanel[] and QubitInfoPanelGray[], which accept arbitrary density matrices describing quantized electromagnetic fields and compute a comprehensive suite of quantum information measures including entanglement, mutual information, and entropy. These tools enable systematic investigation of how encoding scheme choices (Binary vs Gray code) and measurement basis selections (Fock vs Phase) affect the observed quantum correlations. Our framework provides researchers with a validated platform to explore representation-dependent quantum properties in field quantization schemes.

We present a comprehensive computational tool for investigating the quantum digitization problem: how to represent continuous electromagnetic field states as discrete qubit registers. The encoding of quantum field states into finite qubit systems is a fundamental challenge in quantum information theory, with significant implications for quantum computing, communication, and metrology. We introduce two Mathematica-based analysis functions, QubitInfoPanel[] and QubitInfoPanelGray[], which accept arbitrary density matrices describing quantized electromagnetic fields and compute a comprehensive suite of quantum information measures including entanglement, mutual information, and entropy. These tools enable systematic investigation of how encoding scheme choices (Binary vs Gray code) and measurement basis selections (Fock vs Phase) affect the observed quantum correlations. Our framework provides researchers with a validated platform to explore representation-dependent quantum properties in field quantization schemes.