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Quantum Communications and Quantum Imaging

Investigating the impact of relative entropy of coherence on end-to-end fidelity in quantum networks under different noise models

Hilal Sultan Duranoglu Tunc, Riccardo Bassoli, Frank H. P. Fitzek, Abebu Ademe Bayleyegn

Published Sep 18, 2025• 3 citations
Publisher

Abstract

Ensuring high end-to-end fidelity is crucial for quantum networks, yet the impact of relative entropy of coherence on end to end fidelity remains unexplored. This study investigates how amplitude damping, and depolarizing noise affect coherence and fidelity as distance increases, with and without entanglement purification. Using Kraus operators, we model noise and compute relative entropy of coherence. By applying curve fitting, we extract coherence decay time and integrate it into the end-to-end fidelity equation, deriving a new analytical expression. Results show that noise models significantly impact fidelity, with purification improving performance but with varying effectiveness. These findings provide new insights into coherence-fidelity relationships, emphasizing the need for coherence-aware strategies in quantum routing.

DOI
10.1117/12.3065761

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Ensuring high end-to-end fidelity is crucial for quantum networks, yet the impact of relative entropy of coherence on end to end fidelity remains unexplored. This study investigates how amplitude damping, and depolarizing noise affect coherence and fidelity as distance increases, with and without entanglement purification. Using Kraus operators, we model noise and compute relative entropy of coherence. By applying curve fitting, we extract coherence decay time and integrate it into the end-to-end fidelity equation, deriving a new analytical expression. Results show that noise models significantly impact fidelity, with purification improving performance but with varying effectiveness. These findings provide new insights into coherence-fidelity relationships, emphasizing the need for coherence-aware strategies in quantum routing.
We investigate how end-to-end fidelity in quantum networks depends on the relative entropy of coherence under amplitude damping and depolarizing noise, as well as how it degrades with an increasing number of swapping operations. Analytical models reveal that while purification improves fidelity, it offers diminishing returns as the number of purifications increases. Our results show that depolarizing noise yields higher fidelity than amplitude damping for the same relative entropy of coherence. This framework enables coherence-aware routing using only fidelity measurements, providing a foundation for future routing protocols in quantum networks.
In quantum networks, routing mechanisms designed to deliver successfully multiple simultaneous requests to the destination under limited channel capacity should simultaneously consider resource usage optimization, entanglement-generation performance, and the quality of the end-to-end delivered entangled states. The routing approaches developed for quantum networks in the literature mostly consider the change in fidelity during routing. However, it should be noted that quantum states with the same fidelity value may have different levels of coherence. In this study, for the first time, a novel routing and purification approach for quantum networks is presented, using the end-to-end (E2E) relative entropy of coherence (REC) together with E2E fidelity to determine the purification level and the feasibility of candidate paths. In our study, the coherence- and fidelity-aware routing algorithm (CAFARA) is proposed. In CAFARA, the BBPSSW purification levels are determined for each candidate path and ordered from the lowest to the highest. This information is stored in a lookup table. Then, the lowest BBPSSW purification level that simultaneously satisfies the requested fidelity, REC, latency, and capacity constraints is selected. The E2E fidelity, REC, and required number of raw Bell pairs mentioned here are all stored together in the previously mentioned lookup table. This lookup table was constructed using imperfect initial Werner states, one-sided amplitude damping, Werner-state twirling, BBPSSW purification, and density-matrix-based entanglement swapping, and all calculations were completed before the routing process. As the final step, CAFARA selects the best path with the highest entanglement generation rate (EGR) from the selected feasible paths. In our study, the FARA-PostREC and FARA-NoREC algorithms were developed for comparison with CAFARA. While the FARA-PostREC algorithm uses the REC constraint during the final validation stage of the request, FARA-NoREC does not use any REC constraint; it uses only fidelity as the quality parameter of the paths and as the parameter for determining the purification level. In our simulations under varying link distance, channel capacity, network size, and request load, CAFARA achieved a better average request success rate than FARA-PostREC by reducing late-stage request drops related to coherence because it also uses REC during the purification-level determination stage while maintaining the required E2E fidelity and REC values. Although FARA-NoREC often accepts more requests and assumes that they are successfully delivered, the average final fidelity (AFF) and average final coherence (AFC) values of the requests considered successful are lower than those of the other algorithms; the AFC does not even satisfy the REC threshold. Overall, CAFARA provides a balanced trade-off between the quality-guaranteed request success rate, latency, purification overhead, and resource consumption.
Quantum networks hold the potential to revolutionize a variety of fields by surpassing the capabilities of their classical counterparts. Many of these applications necessitate the sharing of high-fidelity entangled pairs among communicating parties. However, the inherent nature of entanglement leads to an exponential decrease in fidelity as the distance between quantum nodes increases. This phenomenon makes it challenging to generate high-fidelity entangled pairs and preserve information in quantum networks. To tackle this problem, we utilized two strategies to ensure high-fidelity entangled pairs and information preservation within a quantum network. First, we use closeness centrality as a metric to identify the closest nodes in the network. Second, we introduced the trace-distance based path purification (TDPP) algorithm, specifically designed to enable information preservation and path purification entanglement routing. This algorithm identifies the shortest path within quantum networks using closeness centrality and integrates trace-distance computations for distinguishing quantum states and maintaining end-to-end (E2E) entanglement fidelity. Simulation results demonstrate that the proposed algorithm improves network throughput and E2E fidelity while preserving information compared to existing methods.
Entanglement fidelity quantifies how well a quantum channel preserves the correlations between a transmitted system and an inaccessible reference system. We derive closed-form expressions for the entanglement fidelity associated with several standard quantum noise models, including the random Pauli-X, dephasing, depolarizing, Werner-Holevo, generalized Pauli (Weyl), and amplitude-damping channels. For each model, we express the entanglement fidelity in terms of a general input density operator ρρρ, using Schumacher's Kraus-operator approach, which provides a channel-agnostic recipe applicable to any completely positive trace-preserving (CPTP) map with a finite Kraus representation. We then specialize to a communication scenario in which the source emits a two-letter parametric alphabet, thereby making explicit the dependence of entanglement preservation on both channel and source parameters. The resulting expressions enable direct comparisons of channel performance and rankings for representative families of input states, including common qubit states.
Quantum networks hold the potential to revolutionize a variety of fields by surpassing the capabilities of their classical counterparts. Many of these applications necessitate the sharing of high-fidelity entangled pairs among communicating parties. However, the inherent nature of entanglement leads to an exponential decrease in fidelity as the distance between quantum nodes increases. This phenomenon makes it challenging to generate high-fidelity entangled pairs and preserve information in quantum networks. To tackle this problem, we utilized two strategies to ensure high-fidelity entangled pairs and information preservation within a quantum network. First, we use closeness centrality as a metric to identify the closest nodes in the network. Second, we introduced the trace-distance based path purification (TDPP) algorithm, specifically designed to enable information preservation and path purification entanglement routing. This algorithm identifies the shortest path within quantum networks using closeness centrality and integrates trace-distance computations for distinguishing quantum states and maintaining end-toend (E2E) entanglement fidelity. Simulation results demonstrate that the proposed algorithm improves network throughput and E2E fidelity while preserving information compared to existing methods.
Entanglement fidelity quantifies how well a quantum channel preserves the correlations between a transmitted system and an inaccessible reference system. We derive closed-form expressions for the entanglement fidelity of several standard quantum noise models, including the random Pauli-XXX, dephasing, depolarizing, Werner-Holevo, generalized Pauli (Weyl), and amplitude-damping channels. For each model, we express the entanglement fidelity in terms of a general input density operatorρ{\rho}ρ, using Schumacher's Kraus-operator approach, which provides a channel-agnostic recipe for any completely positive trace-preserving map with a finite Kraus representation. We then specialize to a communication scenario in which the source emits a two-letter parametric alphabet, thereby making explicit the dependence of entanglement preservation on both channel and source parameters. The resulting expressions enable direct comparisons of channel performance and rankings for representative families of input states.