Fidelity of entanglement and quantum entropies: unveiling their relationship in quantum states and channels
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909855536644096 |
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| author | Kumar, Komal Mallick, Bivas Patro, Tapaswini Ganguly, Nirman |
| author_facet | Kumar, Komal Mallick, Bivas Patro, Tapaswini Ganguly, Nirman |
| contents | Entanglement serves as a fundamental resource for various quantum information processing tasks. Fidelity of entanglement (which measures the proximity to a maximally entangled state) and various quantum entropies are key indicators for certifying entanglement in a quantum state. Quantum states with high fidelity are particularly useful for numerous information-theoretic applications. Similarly, states possessing negative conditional entropy provide significant advantages in several quantum information processing protocols. In this work, we examine the relationship between these two indicators of entanglement, both in state and channel regimes. First, we present a comprehensive analysis and characterization of channels that reduce fidelity of entanglement beyond a threshold limit of bipartite composite systems. In this context, we introduce the notion of fidelity annihilating channel and discuss its topological characterization, along with various information-theoretic properties. We then provide a comparison between channels that diminish the fidelity of entanglement and negative conditional entropies, using the depolarizing channel as an illustrative example. In particular, we determine the parameter regimes in which the depolarizing channel belongs to a given family and establish connections among these families of channels. Extending our analysis from channels to the state level, we further examine the relationship between the fidelity of entanglement and various quantum entropies for general two-qubit states. We derive the upper bound on Rényi 2-entropy, conditional Rényi 2-entropy, Tsallis 2-entropy, and conditional Tsallis 2-entropy, in terms of the fidelity of entanglement. Finally, we explore the relationship between relative entropy and the fidelity of entanglement of a two qudit quantum state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fidelity of entanglement and quantum entropies: unveiling their relationship in quantum states and channels Kumar, Komal Mallick, Bivas Patro, Tapaswini Ganguly, Nirman Quantum Physics Entanglement serves as a fundamental resource for various quantum information processing tasks. Fidelity of entanglement (which measures the proximity to a maximally entangled state) and various quantum entropies are key indicators for certifying entanglement in a quantum state. Quantum states with high fidelity are particularly useful for numerous information-theoretic applications. Similarly, states possessing negative conditional entropy provide significant advantages in several quantum information processing protocols. In this work, we examine the relationship between these two indicators of entanglement, both in state and channel regimes. First, we present a comprehensive analysis and characterization of channels that reduce fidelity of entanglement beyond a threshold limit of bipartite composite systems. In this context, we introduce the notion of fidelity annihilating channel and discuss its topological characterization, along with various information-theoretic properties. We then provide a comparison between channels that diminish the fidelity of entanglement and negative conditional entropies, using the depolarizing channel as an illustrative example. In particular, we determine the parameter regimes in which the depolarizing channel belongs to a given family and establish connections among these families of channels. Extending our analysis from channels to the state level, we further examine the relationship between the fidelity of entanglement and various quantum entropies for general two-qubit states. We derive the upper bound on Rényi 2-entropy, conditional Rényi 2-entropy, Tsallis 2-entropy, and conditional Tsallis 2-entropy, in terms of the fidelity of entanglement. Finally, we explore the relationship between relative entropy and the fidelity of entanglement of a two qudit quantum state. |
| title | Fidelity of entanglement and quantum entropies: unveiling their relationship in quantum states and channels |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.11506 |