An improved quantum anonymous notification protocol for quantum-augmented networks

Abstract

Current quantum networks remain difficult to scale because quantum components are noisy, expensive, and resource constrained, which limits the practical security advantages they can provide over classical network infrastructure. Quantum-augmented networks address this challenge by selectively integrating quantum primitives into classical communication systems. Within this setting, quantum anonymous notification provides a way to inform a receiver of an incoming quantum communication without exposing unnecessary metadata. In this work, we propose an improved quantum anonymous notification protocol that uses rotation operations on shared Greenberger-Horne-Zeilinger states to generate anonymous notifications in an n-user quantum-augmented network. We evaluate the protocol under channel-noise conditions and compare its false-notification behavior with earlier notification approaches. The modified protocol shows improved resilience to false notifications under the considered noise model while preserving the anonymity goals of the notification process. We further discuss how this notification layer can support machine-learning-assisted quantum-augmented networks by enabling receivers to prepare for quantum-payload handling without relying on context-bearing packet headers. This reduces header-based information leakage and limits targeted interference at compromised switches, making anonymous notification a useful coordination layer for practical hybrid quantum-classical networks.

1 Introduction

Quantum communication is one of the key aspects of the quantum internet, similar to how communication is an integral part of the current age internet. Current age quantum internet research faces several scalability issues that are similar to early models of the internet. In addition to scalability issues, the practical realization of quantum protocols faces several hardware issues. All the initial work regarding quantum key distribution (QKD) protocols, such as BB84 (Bennett and Brassard, 1984) and B92 (Bennett, 1992), is based on ideal single-photon sources. However, ideal single-photon sources are not practical. This has been worked out by using other imperfect single-photon sources, such as heralded spontaneous parametric down-conversion (SPDC), to simulate single-photon sources (Yuan et al., 2016). Several works pointed out the usefulness of the multiphoton approach as a possible solution to challenges associated with single-photon sources (Burr et al., 2022; Pont, 2023; Jha et al., 2025a). Multiphoton QKD protocols have been studied as a possible solution to noise such as decoherence, bit-flip, and phase-flip (Jha et al., 2024a). However, problems associated with the multiphoton approach include a higher risk of siphoning attacks and lower key rates due to increased occupancy of bandwidth (the same number of bits has more corresponding qubits), etc. (Jha et al., 2025b). Therefore, we must study other possible solutions to noise in quantum devices that can address both the security and scalability issues. One such approach can be designing quantum communication protocols that have inbuilt error correction codes (Jha et al., 2024b).

Quantum-augmented networks (QuANets) are a recent development leading to a scalable and practical idea of a global quantum internet that combines several quantum primitives, such as quantum anonymous notification (QAN) protocols, quantum key distribution, and quantum secure direct communication, into several currently existing classical infrastructures (Pan et al., 2024). As quantum components remain plagued by noise, such as decoherence and attenuation, the scalability of purely quantum networks is severely limited. These noises reduce the fidelity of the quantum states over large distances. The preliminary QuANet model used in this article was proposed by Jha et al. (2024c). Figure 1 describes the working of this model. It consists of three stages (Jha et al., 2024c): (1) An ML classifier assigns a privacy label to each message, determining whether there is any private content, (2) selectively encrypting the message using quantum encryption if it has any private content, (3) transmitting the message packet, which then reaches its destination. The outgoing packet in this method consists of the following parts: (1) a header, which considers information regarding classical or quantum encryption and addresses, and (2) a payload, which can be a quantum-encrypted or classical-encrypted payload. There are certain core vulnerabilities of this approach, especially in the case of networks having compromised switches.

Jha et al. (2024c). The work presents the idea of using machine learning algorithms to selectively classify communication messages in “private” and “non-private” classes. This allows only using quantum encryption for private classes and saves resources for non-private messages. In the diagram, the red arrow indicates the flow of private/quantum encryption information, and the green arrow indicates the flow of non-private/classical-encrypted information.

A critical vulnerability in this QuANet arises from the possibility of compromised switches. In a practical network, we must assume the presence of several compromised switches and a limited number of trusted switches. Considering the above model of QuANet, we consider the class of attacks performed by compromised switches. For example, if we include information on a packet header containing quantum payload, then an attacker can use this information to flag packets having sensitive information, leading to traffic inference attacks. An adversary can selectively attack packets that have a quantum payload by either delaying or dropping them. Attacks could also be based on network monitoring rather than active attacks. Therefore, the practical realization of QuANets depends not only on the robust quantum encryption techniques but also on mitigating several network-level attacks as mentioned above.

1.1 Related works

Based on the above-mentioned issues, we introduce the use of the quantum anonymous notification (QAN) protocol as an extra layer in the quantum-augmented network framework. A general QAN protocol allows a user in the network to anonymously notify any other user in the network using pairs of pre-shared Greenberger–Horne–Zeilinger (GHZ) states (Khan and Shin, 2020). Several earlier works explore anonymous primitives for quantum networks from both theoretical and experimental perspectives, including notification, collision detection, and anonymous message transmission (Khan and Shin, 2020; de Jong et al., 2023; Rückle et al., 2023; Grasselli et al., 2022; Yang et al., 2021; Huang et al., 2022; Unnikrishnan et al., 2019; Gong et al., 2022).

Khan and Shin (2020) proposed one of the popular formalizations of QAN, relying on GHZ correlations to establish sender anonymity while ensuring message delivery. However, these early approaches were primarily theoretical and did not account for realistic imperfections in the physical layer, such as photon loss, depolarizing noise, or detector inefficiencies. In realistic optical and fiber-based networks, photon loss, dephasing, depolarizing noise, and detector inefficiencies degrade the quality of multipartite entanglement, which can directly affect the false-notification probability and, thus, complicate anonymity verification at a larger network scale. This practical gap motivates follow-on efforts that (i) revise the entanglement resource, (ii) formalize better and more robust security and correctness notions, or (iii) demonstrate feasibility based on deployed network infrastructure, that is, analysis under some basic noise models.

A major line of work explores anonymous conference key agreement (ACKA) and other related multi-party anonymity primitives as notification-adjacent building blocks. For example, De Jong et al. (2023) proposed ACKA using linear cluster states constructed over repeater-like chains, emphasizing practical network resource assumptions in which nodes only need neighbor entanglement rather than a central GHZ distributor. Rückle et al. (2023) demonstrated an experimental demonstration of ACKA using four-photon linear cluster states and explicitly optimize protocol parameters under finite-size and noise considerations. Grasselli et al. (2022) demonstrated that GHZ-based protocols can outperform protocols generally based on bipartite entanglement states and provide stronger anonymity guarantees. Another work by Yang et al. (2021) introduced anonymous quantum transmission mechanisms that rely on EPR-based entanglement distribution, enabling message transfer without revealing sender or receiver identities.

Large-scale feasibility has also been demonstrated in city-scale experiments involving up to eight users, showing the potential of GHZ and cluster-state-based architectures for practical anonymous communication (Huang et al., 2022). Some other works proposed one of the first realistic implementations of anonymous quantum communication under noise, showing how anonymity can be preserved even with imperfect entanglement (Unnikrishnan et al., 2019). Gong et al. (2022) presented a W-state-based anonymous communication framework that incorporates both notification and collision detection sub-protocols, directly aligning with the goals of QAN systems. Zheng and Gong (2024a) investigated collision (Zheng and Gong, 2024b) detection in multi-user networks by leveraging higher-partite entangled states, highlighting how quantum resources can enable contention-free medium access in anonymous communication settings. Such a collision detection and notification framework is quite relevant in terms of QuANet-like deployment, where we assume the quantum resources are scarce. In this regime, coordination is the first constraint, and badly designed control signaling can leak important metadata that can risk the anonymity of the entire network.

This remainder of this article is structured as follows. Section 2 defines the quantum anonymous protocol and provides a test case showing the working of this protocol. In this section, we also present simulation results for the working of the QAN protocol, a comparison of the accuracy of our improved QAN protocol with older approaches under noise models, and analyze two possible attacks on this system. Section 4.1 integrates the idea of quantum-augmented networks with the use of a quantum anonymous protocol, providing a foundation for future work on integrating these ideas into a full communication stack.

2 Methods

2.1 The quantum anonymous notification protocol

Several approaches to quantum networks are based on quantum voting (Vaccaro et al., 2007; Li et al., 2021; Arapinis et al., 2021), quantum secret sharing (Hillery et al., 1999; Gottesman, 2000; Senthoor and Sarvepalli, 2022), quantum conference agreement (Murta et al., 2020; Pickston et al., 2023), etc. Early works regarding the quantum internet (Kimble, 2008) were based on the ideas mentioned above. One key aspect of any communication network is preserving user privacy. Even in the case of quantum internet, we must utilize different privacy-preserving techniques to guarantee private communications. A quantum anonymous notification protocol allows a sender to notify the intended receiver of an incoming communication while preserving the identity of the involved parties. Earlier works on QANs focus mainly on preserving the identity of either the receiver or the sender; however, we propose a modified QAN protocol that preserves the identity of both users.

In an earlier work (Khan and Shin, 2020), the authors propose an anonymous quantum private comparison protocol in an -node quantum network using quantum anonymous notification protocol (QAN). In this work, we modify the QAN protocol such that instead of using two unitary operations, we share parts of an angle using secret sharing and then use this to execute the QAN. Apart from this, we apply a layered approach in which each user has two sets of GHZ states, which allows for enhanced anonymity. We also include a study of the working of this modified protocol in the presence of depolarizing noise to simulate realistic hardware setups. The exact details of this modification are as follows,

2.2 Example case: 3-user network

This example can be extended to an -user network, and the generalized protocol is presented in Algorithm 1.

3 Results

In this section, we present the simulation results based on Algorithm 1, with specific parameters presented in Table 1, along with the noise models used, and some possible attacks on the modified QAN system. The values were selected to represent low, medium, and high notification actuation probabilities, respectively, enabling evaluation of protocol behavior across different operating regimes. Before presenting the simulation outcomes, we briefly discuss the theoretical basis underlying the expected results. The notification detection process in the QAN protocol depends on the interference of shared GHZ states, in which local phase rotations determine whether the receiver observes a parity flip. Channel noise, modeled through dephasing and depolarizing effects, reduces the coherence of these GHZ states and thereby lowers the contrast between notification and no-notification cases. The performance of GHZ-based communication schemes is strongly influenced by the fidelity and coherence of the entangled states used, as discussed in earlier works on noisy multipartite entanglement and quantum communication (Guo and Yang, 2023). As coherence decreases, the overall probability of successful notification detection is expected to drop, while false positive events become more likely. The following section presents simulation results that illustrate these effects and highlight the improved robustness of the modified QAN protocol compared to a prior approach.

3.1 Simulation results

For simulation, we focus on the GHZ state shared by the notifier, Alice, in an network. Through these simulations, we present the performance of our proposed QAN protocol and the comparison of the modified QAN protocol to the protocol presented by Khan and Shin (2020). Through the simulations, we present the performance of the modified QAN protocol (in Figure 3), and the performance comparison of the modified QAN protocol with respect to the original QAN protocol under depolarizing noise models (in Figure 4). The other simulation parameters are as follows:

Khan and Shin (2020). The false positive rate is calculated as any notification detected by an unintended party, as a result of different noise models present in the network.

Figure 3 shows the curves for three different values of for increasing numbers of . In this figure, we have plotted the probability of a notification detected by the intended receiver when the sender applied the rotation for receiver index qubit with a probability of , plotted against the number of repetitions of QAN rounds, .

Figure 3 shows that for the increased value of the probability of rotation application, the detection of notification by the receiving party improves significantly. We notice that we can find a middle-ground between increasing values and values to optimize the overall notification detection probability. Figure 5 illustrates that the QAN protocol preserves user anonymity. The axis shows the flipper index, that is, the qubit index for a possible notifier or receiver. The axis shows the outcome index, which shows the combined bit-string obtained by measuring the GHZ state, and the axis presents the probability of different outcome strings when measured by different flipper indices (i.e., users). The protocol achieves a high notification detection rate across various and values while maintaining notifier anonymity, as shown in the figures mentioned above.

3.2 Noise integration

2. Two-qubit depolarizing noise:

While the simulation results focus on a network of users, the proposed QAN protocol naturally generalizes to larger networks. The quantum resource overhead scales as because each of the users distributes one -partite GHZ state. The communication complexity scales quadratically as each user broadcasts measurement outcomes associated with all received GHZ states.

3.3 Attacks

The anonymity of the users participating in the QAN protocol mentioned in the above section can be analyzed for some attacks in which we consider semi-honest participants and compromised users. Here, we show that even if we consider all the users in the network to be semi-honest, the anonymity of any sender and receiver is preserved.

3.3.1 Assuming semi-honest parties

We assume the set of users to be . For each user , we consider a partite GHZ state represented as follows:which is prepared and distributed by user . The user has an associated secret mapping , which lets them know which qubit belongs to which user in the system. This can be written as

This shows the mapping (bijective mapping) of each qubit in belongs to one user. This mapping, as mentioned, is only known to the distributor, .

Now, we consider a general notifier, , and a general receiver, . The user will use , that is, the state they distributed. For the secret mapping, , there exists a unique index, , such that

During the QAN stage, every party modifies its qubit by applying a rotation operator (), where is the secret share of angle distributed to each user in the network. However, the notifier modifies the rotation on her qubit in position by applying a rotation of with a probability of . All other parties, upon receiving their qubits from , apply the standard .

After the Hadamard gate application and measurement is taken (in computational basis), all parties declare the result for the qubit, that is, every other qubit except their index. Let be the measurement outcome for qubit, so the global parity is defined as

In an ideal no-noise scenario, for the no-notification case, , with a high probability. However, for a case when notifier wants to notify , the changes to 1 with some probability. It is important to note here that only the receiver can identify the parity change for the qubit associated with them. Even if semi-honest users, that is, users who try to gain information from publicly shared data, are not able to identify any local parity change, which only can calculate.

3.3.2 Compromised user

Consider a network with compromised users, such that . We consider one of the compromised users to be . A similar argument can be used to show that the anonymity of the sender and receiver is preserved, unless the compromised party is the sender. However, even in this case, where is the sender, the only information she can gain by publication announcement is the index of the receiver. However, no further information can be obtained by outsiders, even if half of the users in the system are compromised because each user has a different secret mapping.

However, a system with many compromised users can cause some issues with the overall working of the system. Because the QAN step comes before transmission of an actual quantum-encrypted message, a compromised node can apply random rotations to random indices to disrupt the overall parity of the system. Thus, this disruption must be taken care of in the long run for practical deployments.

In practical hardware implementations, the fidelity of shared GHZ states may degrade due to gate errors, loss, and decoherence. A small decrease in initial fidelity would slightly lower the contrast between the notification and no-notification cases. This means the detection probability decreases marginally, while the false positive rate shows a small increase. Although a detailed quantitative analysis is beyond the scope of the current article, this trend follows the expected behavior of multipartite GHZ states under noise-heavy conditions and emphasizes the importance of maintaining high state-preparation fidelity for reliable network performance.

4 Discussion

A modified QAN protocol has been presented in this work. Its performance has been validated through several experiments, and security under several plausible attacks has also been studied. Now, we will discuss how this QAN protocol can be integrated with the QuANet framework, such that we can achieve some protection from compromised switches in a network by achieving switch independence.

4.1 Integrating QAN with the QuANet framework

Jha et al. (2024c). The diagram is divided into two parts: (1) the part outlined in the blue box outlines the protocol that is executed before actual transmission, and (2) the red arrows mark the transmission and encryption method. In the first half of the protocol, Alice obtains a privacy label for her message, and based on that, she either initiates the QAN protocol or she uses classical encryption techniques (for example, AES, etc.) to transmit her message to Bob. Once QAN is performed (for private messages), we move on to the transmission phase. In this phase, if QAN was used, either Alice and Bob start a QKD run, or Alice sends a packet with a quantum payload to Bob immediately after the notification.

The integration of the QAN protocol with the QuANet framework is formally presented in Algorithm 2. The protocol begins with an ML-based decision procedure that evaluates the privacy level of a composed message M. If the message is classified as non-private (L = 0), classical encryption is applied before transmission. Otherwise, if the message is deemed private (L = 1), the quantum anonymous notification (QAN) protocol is invoked.

By using this integrated approach to a quantum-augmented network, the protocol achieves switch independence, which is particularly beneficial in cases where there are compromised switches in the system. This also allows us to remove any information from the packet headers that identifies any packets with private contents, that is, a quantum-encrypted payload. This would help us reduce any directed attacks by adversaries as a result of these compromised switches in the network.

4.2 Conclusion

In this work, we presented an improved QAN protocol that can be easily integrated with a QuANet framework. The proposed QAN protocol uses quantum secret sharing to establish a secret share of the angle that every user in the system holds, which is then modified by any sender to anonymously notify the receiver using pre-shared GHZ states. The integration of QAN with the QuANet framework allows us to modify the pre-proposed structure of message packets, such as headers and payload. The header information from these packets can be exploited by compromised switches to gain some contextual information as this framework uses selective quantum encryption for messages containing private information. The adversaries can thus use such information to either delay or drop these packets at these compromised switches. Use of QAN before actual transmission would allow the receivers to bypass incoming messages from the switches and also help in reducing the information that is provided in the headers. This is what we call switch independence.

The simulation results in Figures 3, 5 show that the QAN protocol achieves decent notification detection probability even for smaller rounds . We also present a comparison of the working of our QAN protocol to one of the earlier defined approaches under several noise models. From Figure 4, we can see that the false positive rate for notification detection is significantly different (approximately for any ) for our approach vs. the older one. We also present an analysis for two possible attack scenarios for our QAN protocol and show that the anonymity of the sender–receiver pair is maintained even in the case of all users being semi-honest or users in the system being compromised.

Future work can focus on active attacks, such as rotation poisoning or targeted gate attacks. For example, we consider the last-speaker steering attack. Here, an adversary holds on till they can see others’ broadcasts and then chooses their bit to cause the final parity changes. These attacks can be further avoided by providing each party with certifications and signatures to avoid this class of attacks. If we consider the case of a rotation poisoning attack by a single compromised node that slightly perturbs its local rotation each round, we notice that the shared GHZ coherence degrades, false notification events become more likely, true notifications are harder to confirm, and convergence slows as the network size increases. A simple mitigation is to randomize local bases across rounds, watch for sudden decreases in measured coherence, and aggregate a few rounds by majority vote so one misbehaving node cannot drive the outcome.

These modifications to the QuANet architecture not only increase the overall security of the system but also provide us with a scalable and more robust framework than the stand-alone QuANet framework. Future work can look at network simulation for this work to gain more insights into possible bottlenecks and shortcomings in a fully-fledged network scenario. There are, however, some limitations of this work that must be further studied. These limitations include analysis of fidelity of sharing GHZ states under noise-heavy hardware, a more thorough analysis of the performance of switch independence in different network configurations, and thus, development of any further protocols, which can streamline the integration of our QAN protocols with other quantum secure direct communication (QSDC) protocols necessary for quantum secure communication (Sun et al., 2025; Zou and Qiu, 2014). In addition, the modified QAN can be used in the development of quantum-augmented microgrid structures, where we integrate the use of quantum components such as quantum key distribution, quantum anonymous notification, and quantum random number generation to develop a secure quantum-augmented microgrid.

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