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Updated: May 30, 2026
07:56
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
Causality and the complete positivity of classical polarization maps
1Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario M5S 1A7, Canada. ogamel@physics.utoronto.ca
Optics Letters
|August 3, 2011
Summary
This study mathematically proves how to represent general physical transformations of light polarization using an ensemble of Jones matrices. The derivation ensures a rigorous foundation for optical polarization analysis.
Area of Science:
- Optics and Photonics
- Mathematical Physics
- Quantum Information Theory
Background:
- Mueller and Jones matrices are established mathematical tools for describing light polarization.
- The representation of general polarization transformations as an ensemble of Jones matrices is widely used but lacks rigorous proof.
Purpose of the Study:
- To provide a formal derivation for the representation of the most general physical transformation on the polarization state of light.
- To establish a rigorous mathematical foundation for the ensemble of Jones matrices representation.
Main Methods:
- Derivation from fundamental physical principles.
- Application of the matrix theory of positive maps.
Main Results:
- A rigorous derivation of the expression ∑iV(i)ΦV(i)(†) for general polarization transformations.
- Confirmation that this representation is grounded in physical principles and mathematical theory.
Conclusions:
- The ensemble of Jones matrices representation for general polarization transformations is mathematically validated.
- This work provides a foundational proof for a commonly assumed result in optical polarization studies.
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