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A Fisher Information-Based Incompatibility Criterion for Quantum Channels
Qing-Hua Zhang1,2, Ion Nechita2
1School of Mathematical Sciences, Capital Normal University, Beijing 100048, China.
Entropy (Basel, Switzerland)
|June 24, 2022
Summary
We developed a new quantum Fisher information criterion to detect incompatibility in quantum channels. This method provides analytical conditions for Schur channels and reveals insights into depolarizing channel structures.
Area of Science:
- Quantum Information Theory
- Quantum Measurement Theory
- Quantum Channel Characterization
Background:
- Quantum channels describe information transmission, and their properties are crucial for quantum technologies.
- Incompatibility of quantum operations is a key concept, limiting achievable precision and information transfer.
- Existing criteria for channel incompatibility are often limited in scope or analytical tractability.
Purpose of the Study:
- To introduce a novel incompatibility criterion for quantum channels.
- To establish analytical conditions for the incompatibility of specific quantum channels, namely Schur channels.
- To explore the incompatibility structure of multiple depolarizing channels and compare it with existing methods.
Main Methods:
- The study utilizes the concept of quantum Fisher information to construct the new incompatibility criterion.
- The criterion is applied to analyze the incompatibility of pairs of Schur channels.
- The incompatibility of multiple depolarizing channels is investigated and compared with results from asymmetric quantum cloning.
Main Results:
- A new criterion for detecting quantum channel incompatibility based on quantum Fisher information is presented.
- The first analytical conditions for the incompatibility of two Schur channels are derived.
- The incompatibility structure of a tuple of depolarizing channels is characterized, showing consistency with known results.
Conclusions:
- The proposed quantum Fisher information-based criterion offers a powerful tool for quantifying and detecting quantum channel incompatibility.
- The findings provide new analytical insights into the behavior of Schur and depolarizing channels.
- This work contributes to a deeper understanding of fundamental limitations imposed by channel incompatibility in quantum information processing.
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