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Updated: Nov 3, 2025
07:56
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
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Interpolating between Positive and Completely Positive Maps: A New Hierarchy of Entangled States
Katarzyna Siudzińska1, Sagnik Chakraborty1, Dariusz Chruściński1
1Faculty of Physics, Astronomy and Informatics, Institute of Physics, Nicolaus Copernicus University, ul. Grudziądzka 5/7, 87-100 Toruń, Poland.
Entropy (Basel, Switzerland)
|June 2, 2021
Summary
A new class of positive maps offers novel characterizations for entangled quantum states. This research refines existing entanglement measures, including the Schmidt number, with applications to qubit systems.
Area of Science:
- Quantum Information Theory
- Quantum Entanglement
- Quantum Maps
Background:
- Positive maps and completely positive maps are fundamental concepts in quantum information.
- Entangled states are a key resource in quantum information processing.
- The Schmidt number is a well-established measure for quantifying entanglement.
Purpose of the Study:
- Introduce a new class of positive maps that bridge the gap between positive and completely positive maps.
- Develop a new method for characterizing entangled quantum states.
- Refine existing entanglement measures based on the Schmidt number.
Main Methods:
- Introduction of a novel class of positive maps.
- Development of a new characterization for entangled states using these maps.
- Application and illustration using qubit systems.
Main Results:
- A new class of positive maps interpolating between positive and completely positive maps is established.
- This new class provides a novel characterization of entangled states.
- A refinement of entanglement characterization using the Schmidt number is achieved.
Conclusions:
- The introduced positive maps offer a new perspective on quantum entanglement.
- This work provides a more nuanced understanding and quantification of entangled states.
- The findings have potential implications for quantum information processing and quantum technologies.
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