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Physica Scripta

Performance of quantum networks over time-varying amplitude damping channels with repeater and multiple sending nodes

Anas M. Salhab

Published Jan 8, 2026• 0 citations
Publisher

Abstract

Abstract In this paper, we consider an efficient dual-hop quantum communication network with multiple senders or nodes, a repeater, and a receiver. We derive closed-form expressions for the system quantum outage probability (QOP) assuming time-varying amplitude damping (TVAD) quantum channels. In addition, closed-form expressions for the quantum hashing outage probability of two approximated quantum channels, namely TVAD Pauli twirl approximated (TVADPTA) and TVAD Clifford twirl approximated (TVADCTA) channels are also provided. These channels are efficient in modeling the simplest kind of noise in quantum devices. Opportunistic node scheduling is proposed, for the first time, to select among sending nodes, where the node of the largest relaxation time T 1 is allowed to transmit to repeater, which in turn communicates with receiver. The impact of various system parameters, including number of sending nodes K , coefficient of variation of relaxation time ϵ , code rates of both hops, channel damping parameter γ , and channel noise limit γ l ( R ) on the system performance is investigated. Findings show that for the case where first hop is dominating the system performance, the more the number of nodes, the better the achieved performance. This gain starts to vanish once the second hop starts dominating the system performance. For good quality channels, more nodes are needed in order for second hop to dominate the system performance compared to the case of low quality channels. Finally, results illustrate that for higher values of ϵ , and in order to achieve a certain target QOP, both nodes and repeater need to adapt their transmission rates to the optimum values.

DOI
10.1088/1402-4896/ae35b1

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Abstract In this paper, we consider an efficient dual-hop quantum communication network with multiple senders or nodes, a repeater, and a receiver. We derive closed-form expressions for the system quantum outage probability (QOP) assuming time-varying amplitude damping (TVAD) quantum channels. In addition, closed-form expressions for the quantum hashing outage probability of two approximated quantum channels, namely TVAD Pauli twirl approximated (TVADPTA) and TVAD Clifford twirl approximated (TVADCTA) channels are also provided. These channels are efficient in modeling the simplest kind of noise in quantum devices. Opportunistic node scheduling is proposed, for the first time, to select among sending nodes, where the node of the largest relaxation time T 1 is allowed to transmit to repeater, which in turn communicates with receiver. The impact of various system parameters, including number of sending nodes K , coefficient of variation of relaxation time ϵ , code rates of both hops, channel damping parameter γ , and channel noise limit γ l ( R ) on the system performance is investigated. Findings show that for the case where first hop is dominating the system performance, the more the number of nodes, the better the achieved performance. This gain starts to vanish once the second hop starts dominating the system performance. For good quality channels, more nodes are needed in order for second hop to dominate the system performance compared to the case of low quality channels. Finally, results illustrate that for higher values of ϵ , and in order to achieve a certain target QOP, both nodes and repeater need to adapt their transmission rates to the optimum values.
Recent experimental studies have shown that the relaxation time T1{T}_{1}T1​ and the dephasing time T2{T}_{2}T2​ of superconducting qubits fluctuate considerably over time. Time-varying quantum channel (TVQC) models have been proposed in order to consider the time-varying nature of the parameters that define qubit decoherence. This dynamic nature of quantum channels causes a degradation of the performance of quantum error correction codes (QECCs) that is portrayed as a flattening of their error rate curves. In this article we introduce the concepts of quantum outage probability and quantum hashing outage probability as asymptotically achievable error rates by a QECC with the quantum rate RQ{R}_{Q}RQ​ operating over a TVQC. We derive closed-form expressions for the family of time-varying amplitude damping channels and study their behavior for different scenarios. We quantify the impact of time variation as a function of the relative variation of T1{T}_{1}T1​ around its mean. We conclude that the performance of QECCs is limited in many cases by the inherent fluctuations of their decoherence parameters and corroborate that parameter stability is crucial to maintain the excellent performance observed over static quantum channels.
At the heart of building a large-scale quantum internet lies the challenge of establishing long-distance entanglement using quantum repeaters, which mitigate direct transmission losses but introduce additional noise in the nodes via interactions with the environment and imperfect operations. This effect has typically been studied under a simplifying Pauli channel assumption. Our study focuses on distributing end-to-end entanglement in a homogeneous, repeater-based linear quantum network operating under a non-Pauli noise, specifically, amplitude damping noise, which we refer to as amplitude damping-affected quantum network (AQN). Unlike its twirled counterpart (TAQN), where the resulting state is fully Bell-diagonal with a single parameter, we prove that the AQN produces a block-diagonal state in the Bell basis with four parameters. We develop a method for the simulation of AQN, where we keep track of these four parameters of each entangled link, along with the number of times noise acts on it, i.e., its age, until it is consumed for swapping. Our results reveal that across diverse policies, including NESTING and SWAP-ASAP, AQN consistently outperforms TAQN in terms of both fidelity and average entanglement. The benefit is most significant in the low-probability regime of elementary link generation, highly relevant for near-term experiments. Notably, we also identify the coherence-time and link-probability regions where TAQN fails while AQN succeeds in distributing end-to-end entanglement.
The optimal relay path calculation and selection are important factors to affect the performance of quantum communication network. Current researches seldom consider the quantum path selection in real noisy environments. One of the difficult problems is how to analyze the influence of the noise on the quantum communication in multi-hop channels. This paper aims to solve the path selection problem of the quantum teleportation network in noisy environments. The process of entanglement swapping in the phase damping channel is first studied with an example of two-hop quantum channel, whose damping factors are p1 and p2. The entanglement states |φ> 12+ and |φ> 34+ are distributed separately in each hop. After the entanglement swapping, the density matrix of the entanglement state of photon 1 and photon 4 is obtained by performing a partial trace over the environment. Then, the Bures fidelity of this entanglement is calculated. After that, we define the path equivalent damping factor to describe the characteristic of the two-hop noisy quantum relay path. With an equivalent calculation method, the results above can be generalized to multi-hop channel. The path equivalent damping factor of the multi-hop amplitude damping channel is also obtained. According to these results, we propose an optimal relay protocol for the quantum teleportation network with the criterion of path equivalent damping factor, which means that a relay path with the minimum path equivalent damping factor can obtain the highest teleportation fidelity. The types and parameters of the messages used in the protocol are given. The processes of the relay protocol are described specifically, including neighbor finding, quantum link noise measurement, and quantum link status transmission. An improved Dijkstra algorithm is used in the optimal path calculation. Furthermore, because the entanglement resources maintained in the quantum nodes are limited and may be exhausted in superior quantum links, we propose a resource reservation method to avoid the failure of the relay path setup. Theoretical analysis and simulation show that our method can obtain a lower average equivalent damping factor and higher teleportation fidelity. It can also be seen that increasing the number of the entanglement resources will raise the performance of the quantum network, however, it brings higher cost and complexity. Therefore, the entanglement resources maintained in the quantum nodes must be configured reasonably according to the network scale, the cost, the time delay and the need of the users.
We give the detailed processes for sharing a four-qubit pure entangled state as quantum channel in amplitude damping (AD) network channel via entanglement compensation.We propose a secure (2,2)-type quantum teleportation (QT) scheme based on this AD network channel, which allows 2-dimensional quantum information shared by 2 senders to be teleported to 2 receivers in such a way that after performing two Bell-state measurements by two senders, the original target state can be probabilistically reconstructed through introducing an auxiliary qubit and executing appropriate local unitary operations provided that all the receivers collaborate. We then extend it to the transmission of a 2-dimensional quantum secret state shared by n senders to m receivers (i.e., (n,m)-type QT of shared 2-dimensional quantum secret) from the perspectives of projective measurement, positive-operator-valued measurement (POVM) and generalized Bell-state measurement. Furthermore, we generalize the above (n,m)-type QT to the case of transmitting a shared d-dimensional quantum secret state. Our approach enables efficient and distributed quantum information relay, eliminating the need for a fully trusted central or intermediary node. The results show that our schemes achieve unit fidelity, though the success probabilities are less than 1. More interestingly, the QT protocol for high-dimensional quantum states exhibits a higher success probability than low-dimensional states under equivalent AD conditions.
We propose a protocol for multipartite secret sharing of quantum information through an \textit{amplitude damping} quantum channel. This network is, for example, of two organizations communicating with their own employees connected via classical channels locally. We consider a GHZ state distributed among four members in an asymmetric fashion where the members of a sub-party collaborate to decode the received information at their end. The target is to send two bits of information in \textit{one execution} of the protocol. Firstly, we consider an ideal channel and observe that our protocol enables decoding of a secret 2-bit information with unit probability. This is accomplished by one of the senders by the use of a globally operated \textit{quantum teleportation operator}. Secondly, we implement the same protocol in a realistic scenario under energy dissipation by the use of a parameterized \textit{amplitude damping channel} with variable noise. This noise is associated with energy dissipation and hence, loss of probability to distinguish and decode the information at the receiving end. Finally, we make this task possible through an optimization algorithm. Various channel \textit{quality measures} are also quantitatively ascertained.
Abstract The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of both the ultimate capacities of quantum channels and the efficiency of imperfect quantum repeaters. In this work, using a recently developed node-splitting technique which introduces internal losses and noise into repeater devices, we present achievable end-to-end rates for noisy-repeater quantum networks. These are obtained by extending the coherent and reverse coherent information (single channel capacity lower bounds) into end-to-end capacity lower bounds, both in the context of single-path and multi-path routing. These achievable rates are completely general, and apply to networks composed of arbitrary channels arranged in general topologies. Through this general formalism, we show how tight upper-bounds can also be derived by supplementing appropriate single-edge capacity bounds. As a result, we develop tools which provide tight performance bounds for quantum networks constituent of channels whose capacities are not exactly known, and reveal critical network properties which are necessary for high-rate quantum communications. This permits the investigation of pertinent classes of quantum networks with realistic technologies; qubit amplitude damping networks and bosonic thermal-loss networks.