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Updated: Jul 24, 2025
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
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Rényi Entropy, Signed Probabilities, and the Qubit
Adam Brandenburger1, Pierfrancesco La Mura2, Stuart Zoble3
1Stern School of Business, Tandon School of Engineering, NYU Shanghai, New York University, New York, NY 10012, USA.
Entropy (Basel, Switzerland)
|July 8, 2023
Summary
This study characterizes qubit states using an entropic uncertainty principle on a phase space. It employs Rényi entropy to define quantum mechanics, advancing foundational quantum information science.
Area of Science:
- Quantum Information Science
- Quantum Mechanics Foundations
- Mathematical Physics
Background:
- Qubit states are fundamental to quantum information.
- Axiomatizing quantum mechanics requires characterizing these states.
- Existing frameworks may benefit from novel mathematical approaches.
Purpose of the Study:
- To characterize qubit states within quantum mechanics.
- To contribute to the axiomatization of quantum mechanics.
- To explore the application of entropic uncertainty principles.
Main Methods:
- Utilized an eight-point phase space formulation.
- Employed Rényi entropy, a generalization of Shannon entropy.
- Defined entropy for signed phase-space probability distributions.
Main Results:
- Successfully characterized qubit states using the entropic uncertainty principle.
- Demonstrated the utility of Rényi entropy in this context.
- Provided a new perspective on quantum state representation.
Conclusions:
- The entropic uncertainty principle offers a powerful tool for characterizing quantum states.
- Rényi entropy is suitable for analyzing signed phase-space distributions.
- This work advances the axiomatization program in quantum mechanics.
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