Fidelity of entanglement and quantum entropies: unveiling their relationship in quantum states and channels
arXiv:2506.11506 · doi:10.1140/epjp/s13360-025-06941-6
Abstract
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.
arXiv comment23 pages, 1 Table, Close to published version
References in corpus (56)
- Quantum entanglement
- Quantum Cryptography
- Quantum secret sharing
- Entanglement detection
- Quantifying Entanglement
- How to share a quantum secret
- Remote State Preparation
- Bell Inequalities and the Separability Criterion
- One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
- On quantum Renyi entropies: a new generalization and some properties
- Minimum cbits for remote preperation and measurement of a qubit
- Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
- General Entanglement Breaking Channels
- Quantum information can be negative
- Negative entropy and information in quantum mechanics
- Entropic uncertainty relations - A survey
- Entanglement as precondition for secure quantum key distribution
- EPR Steering Inequalities from Entropic Uncertainty Relations
- Quantum state merging and negative information
- Faithful remote state preparation using finite classical bits and a non-maximally entangled state
- Teleportation and Secret Sharing with Pure Entangled States
- Inequalities for Quantum Entropy: A Review with Conditions for Equality
- Characterization of separable states and entanglement witnesses
- Distributed quantum dense coding
- Approximate transformations and robust manipulation of bipartite pure state entanglement
- Quantum conditional operator and a criterion for separability
- Entropic Bell Inequalities
- All quantum states useful for teleportation are nonlocal resources
- Conditional entropies and their relation to entanglement criteria
- The fully entangled fraction as an inclusive measure of entanglement applications
- The structure of Renyi entropic inequalities
- Entanglement witness operator for quantum teleportation
- Incompatibility breaking quantum channels
- Steering Bell-diagonal states
- Geometry of two-qubit states with negative conditional entropy
- Quantifying Quantumness of Channels Without Entanglement
- Entanglement-annihilating and entanglement-breaking channels
- A Note on Fully Entangled Fraction
- Geometry of faithful entanglement
- Witness of mixed separable states useful for entanglement creation
- Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
- Non-negativity of conditional von Neumann entropy and global unitary operations
- Exclusion Principle for Quantum Dense Coding
- Upper bound of the fully entangled fraction
- Witnessing Negative Conditional Entropy
- Maximally entangled state and fully entangled fraction
- Witness for edge states and its characteristics
- On Estimation of Fully Entangled Fraction
- An Upper Bound of Fully Entangled Fraction of Mixed States
- Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps
- Quantum channels that destroy negative conditional entropy
- Quantum conditional entropies and steerability of states with maximally mixed marginals
- Repeater-Based Quantum Communication Protocol: Maximizing Teleportation Fidelity with Minimal Entanglement
- Quantum channels and some absolute properties of quantum states
- On fully entangled fraction and quantum conditional entropies for states with maximally mixed marginals
- Information theoretic resource-breaking channels