Abstract
Semi-quantum dialogue (SQD) enables secure bidirectional communication even when one participant has limited quantum capabilities. In order to solve the problems of low efficiency and quantum resource constraints, an efficient SQD protocol using single-photon is proposed. In the SQD, one communicating party needs to have semi-quantum capabilities to complete the dialogue, which could consume lower quantum resource. Moreover, single photons as quantum channels significantly reduces both preparation and operational costs. Finally, decryption can be performed without any classical disclosure, effectively preventing potential information leakage. Security analysis demonstrates resilience against common attacks, including intercept-resend, measure-resend, entanglement-measurement, and Trojan horse attacks, with no information leakage. Compared with existing semi-quantum dialogue protocols, our proposed protocol consumes fewer quantum resources while achieving higher communication efficiency and enhanced security.
1 Introduction
Quantum communication, a fundamental branch of quantum information science, exploits the uncertainty principle of quantum mechanics to achieve secure communication between distant parties. In 1984, Bennett and Brassard first proposed the quantum key distribution (QKD) protocol [1]. Motivated by the success of QKD, extensive researches have been conducted within quantum information science, such as quantum secret sharing (QSS) [2–4], quantum secure direct communication (QSDC) [5–7] and quantum dialogue (QD) [8–10]. Although QD is developed on the basis of QSDC, significant differences exist between these two communication schemes. QSDC directly transmits secret messages over a quantum channel, typically in a one-way manner. Building on this idea, QD enables the simultaneous two-way exchange of secret messages within a single protocol. However, QD is not equivalent to two rounds of QSDC, as both parties jointly encode their messages on shared quantum states, resulting in distinct protocol structures and security properties.
Nguyen first formulated the concept of QD in 2004 [8], where Bell states were employed for encoding and decoding. Subsequently, extensive research on quantum dialogue has been conducted, leading to the development of several important branches. Among them, controlled quantum dialogue (CQD) [11] achieves equal information exchange between the two parties through a controller, simplifies the entanglement preparation process, and enhances security through hash verification. Measurement-device-independent quantum dialogue (MDI-QD) [12] allows both communicating parties to prepare quantum states while an untrusted third party performs the measurements, ensuring security without requiring quantum memory and providing inherent resistance to memory attacks.
However, most quantum communication protocols still require substantial quantum resources, which hinders the practical deployment of QD protocols. To mitigate this issue, Boyer et al. introduced semi-quantum key distribution (SQKD) in 2007 [13], restricting one participant to classical operations while the other retains full quantum capabilities. Building upon SQKD principles, the first semi-quantum dialogue (SQD) protocol was subsequently proposed [14], which introduces a unified framework of semi-quantum protocols using Bell states, further reducing implementation costs by allowing one party to perform only limited classical operations. Since then, more SQD protocols have been developed. In 2018, Ye et al. proposed two SQD protocols [15] based on single photons, one of which does not require the classical party to possess measurement capabilities, thereby effectively enhancing the flexibility of the protocol. Furthermore, both of the proposed protocols achieve a communication efficiency of 66.7%.
Later, Pan proposed a SQD protocol based on Bell states in 2020 [16], where secure and reliable encoding and exchange of information are achieved through the entanglement collapse of the Bell states. In addition, the classical one-time pad encryption process further improves the security of the protocol. However, a security flaw in Pan’s SQD protocol based on Bell states allows an undetected double controlled-NOT attack. To address this issue, Shi proposed an improved and secure protocol [17] in 2023. In the same year, Shi proposed a SQD protocol using hyperentangled Bell states [18]. Unlike previous SQD protocols, this protocol combines the advantages of SQKD and SQD, introducing a new mode of dialogue and providing a new way of thinking. In 2025, Yang et al. designed a SQD protocol based on GHZ states [19], the protocol does not employ decoy particles and delay-line operations, effectively reducing the overhead for the classical party. In the same year, Li et al. proposed a SQD protocol based on four-particle Ω state [20]. By utilizing the properties of Ω state, the protocol effectively facilitates the exchange of classical information between two parties.
However, on the one hand, the above SQD protocols using single photons require the disclosure of classical messages for decryption, which inevitably affects their efficiency. On the other hand, those SQD protocols using entangled states still suffer from low efficiency and difficulties for the hard prepared entangled-state. In the proposed SQD protocol, Bob encrypts his message using the single-photon sequence sent by Alice, which fundamentally differentiates it from QSDC.
To address these limitations, we propose an efficient semi-quantum dialogue protocol using single-photon. The proposed protocol offers several advantages:
The protocol employs single photons as quantum resources, offering easier preparation and higher transmission efficiency than the QD protocols with entangled states;
The semi-quantum communicating party can only perform classical operations, thereby reducing the quantum device requirements;
The SQD protocol does not require the disclosure of any classical information related to decryption.
The remainder of this manuscript is organized as follows. Section 2 introduces the detailed procedure of the proposed protocol. Section 3 presents the detailed security analysis. Section 4 evaluates the efficiency and compares the proposed protocol with existing protocols. Finally, Section 5 provides the conclusions.
2 Protocol description
The SQD protocol using single-photon involves two participants: the fully quantum party, Alice, who possesses complete quantum capabilities, and the semi-quantum party, Bob, who is limited to performing only a restricted set of operations. They use single photons as the quantum channel for transmitting secret information. The operations available to the semi-quantum party can be classified into the following two modes:
- A.
Detection mode
Measuring the qubits in the Z-basis ;
Preparing the (fresh) qubits in the Z-basis;
Sending or reflecting the qubits without disturbance.
- B.
Communication mode
Preparing the (fresh) qubits in the Z-basis;
Reordering the qubits (via different delay lines);
Sending or reflecting the qubits without disturbance.
The efficient semi-quantum dialogue protocol using single-photon is described as follows.
2.1 Initialization stage
Step 1: Alice and Bob send a binary bit string of length to each other respectively, denoted as , , where .
Step 2: Alice and Bob share classical bits , where . The distribution of “0” and “1” in is uniform and each accounts for half.
Step 3: Alice and Bob share the hash function . The preparation rule of the information particle state is: corresponds to secret information “0”, corresponds to secret information “1”.
2.2 Encryption stage
Step 1: Alice’s process of initial state preparation and encoding. Alice selects all the bits with a value of “0” in the key sequence to form the information particle sequence , where ; correspondingly, Alice selects all the bits with a value of “1” in the key sequence to form the decoy photon sequence , where . Similarly, Bob also formed sequences and in the same way. For each bit in , if , Alice prepares the information particle based on her secret information and the rule , and eventually forms the sequence , then she records the position of each in ; if , Alice randomly prepares a decoy photon from four states and records its initial state. The final sequence is formed as , and Alice records the position of each in . Alice combines sequences and into sequence based on the positions of and in . The possible particles corresponding to each bit in the key sequence are shown in Table 1. To further illustrate Alice’s specific operations, Figure 1 presents an encoding method executed by Alice. Then Alice prepares a new decoy particle sequence , where from four states and randomly inserts into the sequence . She sends the inserted sequence to Bob.
Step 2: The first round of eavesdropping detection. Alice and Bob can install a photon number splitter and wavelength filter in front of their device to prevent the attack of the Trojan horse. After Bob receives the inserted sequence , Alice announces the position of the decoy particle sequence . At this moment, Bob can perform the operations in Detection mode. Then he divides the sequence into and , for each in , Bob randomly selects a Z-basis measurement and, based on the outcome, prepares the same state in the Z-basis. Alternatively, he may simply allow the particle to reflect without introducing any disturbance. After confirming that Alice has received all the particles, Bob discloses his operations and collaborates with Alice to jointly calculate the error rate. When the error rate is lower than the threshold previously negotiated by both parties, Step 3 is executed. Otherwise, the communication will be terminated.
Step 3: Bob’s Encryption Process. After confirming the channel security, for each in , Bob distinguishes whether it belongs to or based on . For each in , Bob performs a Z-basis measurement, records the measurement result , and deduces Alice’s secret information . At this moment, Bob can perform the operations in Communication mode. Then, based on his own secret information and the rule , Bob prepares the information particle in the Z-basis to form the particle sequence , and replaces . For each in , Bob records it as sequence . Alice and Bob calculate based on using the hash function and compare whether the measurement results are consistent. If both parties calculate the same value of , the protocol will proceed; otherwise, it will be terminated. Using the delay line, Bob rearranges all the particles in and based on Alice’s secret information : If , Bob does not perform any operation on particles and ; if , Bob swaps the positions of particles and and records the swapped positions. Bob forms new sequences and , then he merges sequences and into sequence based on the positions of and in . Later he sends to Alice and use the classical channel to send the rearrangement rules to Alice. To further illustrate Bob’s specific operations, Figure 2 presents one possible operation that Bob might perform.
Step 4: The second round of eavesdropping detection. After Alice receives , she decomposes sequence into and based on the positions of and in . Then she restores and based on , and performs corresponding basis measurements on the particles in . If the error rate is lower than the threshold set by both parties in advance, Step 5 is executed; otherwise, the communication will be terminated.
Step 5: Alice decrypts Bob’s secret information. Alice performs Z-basis measurements on the particles in , eventually obtaining Bob’s secret information . Alice and Bob calculate based on using the hash function and compare whether the measurement results are consistent. If the values calculated by both parties are identical, the decrypted message is considered valid; otherwise, it is deemed invalid. The communication process is completed.
TABLE 1
| 0 | 0 | - | |
| 1 | - | ||
| 1 | - | - |
Alice’s encryption and the particles corresponding to .
FIGURE 1
FIGURE 2
To facilitate understanding of the encoding and decoding processes of the protocol, a simplified example (excluding security check) is provided as follows:
Assume that the shared key between Alice and Bob is 101100, Alice’s secret message is 101, and Bob’s secret message is 110. Based on , Alice may prepare the following initial sequence and send it to Bob: , wherein the information particle sequence , the decoy photon sequence , and . Bob can deduce that Alice’s secret information is 101 based on . Subsequently, Bob replaces the sequence with the sequence corresponding to his own secret message , forming the sequence . Based on Alice’s secret information , Bob swaps the positions of and , and and , forming the sequence and sending it to Alice, where , . Alice can restore the sequences and to sequences and , she ultimately deduces Bob’s secret information as 110.
Considering the inevitable influence of noise in actual quantum channels, the protocol can correct errors caused by noise by using error-correcting codes. In Step 1, by using the error-correcting code , Alice can encode her secret information with , and then she prepares as the sequence of information particles . The remaining steps remain unchanged. In Step 3 as well, Bob also uses error-correcting codes to encode his secret message . Ultimately, in this way, both communicating parties can correct errors and decode the original information sequences and .
The flowchart of the protocol is shown in Figure 3:
FIGURE 3
3 Security analysis
This section analyzes the potential security risks of the proposed SQD protocol, including intercept-resend attack, measure-resend attack, entangled-measure attack, and Trojan horse attack. It also considers the possibility of information leakage to ensure the protocol’s overall security. Accordingly, the following evaluation will address these identified threats.
3.1 Intercept-resend attack
Eavesdropper Eve interferes with the communication between Alice and Bob by executing an intercept-resend attack. Eve may intercept and resend the sequence transmitted from Alice to Bob in Step 2. Note that the sequence contains both Alice’s secret information sequence , the decoy photon sequence and decoy photon sequence . First, Eve lacks knowledge of the shared key between Alice and Bob, she cannot determine the positions of the particles belonging to the and sequence. Second, Eve does not know the preparation basis of the decoy photons, Eve has a probability of resending in the Z-basis and a probability of resending in the X-basis , At this point, two scenarios arise: if Bob chooses to measure, decoy photon is in the Z-basis, the probability that Eve passes the detection is , if decoy photon is in the X-basis, Eve can pass the eavesdropping detection in this scenario; if Bob chooses to reflect, Eve has a probability of passing the eavesdropping detection. Eve has a probability of passing the eavesdropping detection. However, when the number of decoy photons n is sufficiently large, the probability of Eve being detected is .
Similarly, Eve may intercept and resend the sequence transmitted from Bob to Alice in Step 4. It is observed that among the particles used for the second eavesdropping detection, approximately are in the Z-basis, while the remaining are in the X-basis. For the Z-basis, Eve’s attack has a probability of to pass the detection; for the X-basis, Eve’s attack has a probability of to pass the detection. Eve has a probability of passing the eavesdropping detection. Therefore, when the number of decoy particles n is sufficiently large, the probability that Eve is detected is .
It can be observed that Eve has a probability approaching 1 of being detected. In summary, the protocol we propose can effectively resist intercept-resend attacks.
3.2 Measure-resend attack
Eve attempts to obtain the secret information of Alice and Bob through a measure-resend attack. Specifically, Eve may intercept the sequence sent to Bob by Alice in Step 2, and perform measurements on the particles, then resend the measured particles to Bob. However, since the sequence is prepared by Alice based on the shared key with Bob, and Eve has no knowledge of the specific value of this key, even if she obtains the measurement results of , she cannot determine whether these results correspond to the secret information or the decoy photons and . Since decoy photons are randomly prepared in the Z-basis or X-basis, assume Eve’s Z-basis measurement on the resent particles may yield outcomes corresponding to the Z-basis or the X-basis, At this point, two scenarios may occur: if Bob chooses to measure, the particle he measures must be the one resent by Eve. This action does not introduce an error rate; if Bob chooses to reflect, Eve measures a decoy photon with the Z-basis, the eavesdropping detection may pass. If Eve measures a decoy photon with the X-basis, there is a probability that her intervention will be detected during Alice’s security check. For each decoy photon, Eve has a probability of passing the eavesdropping detection. However, the probability of Eve being detected is .
Similarly, Eve may measure and resend the sequence transmitted from Bob to Alice in Step 4. It is observed that among the particles used for the second eavesdropping detection, approximately are in the Z-basis, while the remaining are in the X-basis. For the Z-basis, Eve’s attack can pass the detection; for the X-basis, Eve’s attack has a probability of to pass the detection. Eve has a probability of passing the eavesdropping detection. Therefore, the probability that Eve is detected is .
It can be concluded that when n is sufficiently large, Eve has a probability approaching 1 of being detected. Based on the above analysis, the protocol we propose can effectively resist measure-resend attack.
3.3 Entangled-measure attack
Eve attempts to obtain the secret information between Alice and Bob through an entanglement-measurement attack. Specifically, Eve may intercept the sequence sent by Alice to Bob in Step 2 and perform a unitary operation to entangle her own ancillary particles with Alice’s sequence . Eve’s operation may transform the decoy photons into the following form:
In Equations 1–4, , satisfying the normalization condition. and , and represent the final states of Eve’s ancillary particles after unitary evolution, and different quantum states are mutually orthogonal. Eve can obtain Alice’s secret information by measuring her ancillary particle . It can be concluded that if Eve wishes to avoid detection of eavesdropping, she must ensure that and .However, under this condition, , By comparing the expressions, it can be concluded that Eve cannot distinguish between the secret information states and through measurements on her ancillary particle . Therefore, if Eve attempts to steal the secret information of Alice and Bob via an entanglement-measurement attack without being detected, she cannot obtain any meaningful information.
Similarly, Eve may intercept the sequence sent by Bob to Alice in Step 4 and perform a unitary operation to entangle her own ancillary particles with Bob’s sequence . Eve’s entanglement operation may induce changes in all four types of decoy photons. If Eve attempts to extract information by measuring her auxiliary particles without being detected, she still cannot distinguish between states and .
Based on the above analysis, the protocol we propose can effectively resist entanglement-measurement attacks.
3.4 Information leakage
The issue of classical correlation in quantum dialogue mentioned in [21, 22] refers to the potential leakage of approximately half of the secret information through classical channels. According to Shannon entropy theory [23], there are four possible combinations of secret information exchanged between Alice and Bob in each round of communication, each with a probability of . The prior entropy is . Since neither party discloses any content related to the secret information during the protocol, the posterior entropy remains . The mutual information between the communicating parties (Alice and Bob) and Eve is . Therefore, no information is leaked to Eve. Eve cannot attempt to obtain useful information by stealing the public information exchanged between Alice and Bob. In summary, the protocol we designed is resistant to information leakage.
3.5 Trojan horse attack
As noted in [24], Eve may utilize Trojan horse attacks to target the communication channel between Alice and Bob, primarily through delayed photon attack and invisible photon attack. A delayed photon attack involves Eve splitting a photon from a multi-photon pulse without altering the quantum state for eavesdropping purposes, while an invisible photon attack entails Eve injecting ancillary particles such as invisible wavelengths or delayed pulses into the communication devices to illicitly acquire information. To mitigate these threats, both communicating parties must implement filter to prevent unauthorized photon injections and photon beam separator to detect multi-photon anomalies. By integrating these countermeasures, our protocol effectively resists Trojan horse attacks.
3.6 The double CNOT attack
Eve attempts to obtain the secret information of Alice and Bob by using a double CNOT attack. Eve first prepares an auxiliary particle sequence consisting of particles initialized in the state. She then intercepts the sequence sent by Alice to Bob in Step 2 and performs a controlled-NOT (CNOT) operation, using sequence as the control qubits and sequence as the target qubits. Eve attempts to obtain Alice’s secret message by measuring her auxiliary particle sequence . Afterward, Eve forwards the sequence to Bob. Once Bob completes his encoding operation, Eve intercepts the encoded sequence again. She performs a second CNOT operation, taking sequence as the control qubits and sequence as the target qubits. Finally, Eve attempts to extract Bob’s secret message by measuring the auxiliary particle sequence .
However, Eve’s CNOT operations inevitably introduce noise and disturbances into the quantum channel, thereby altering the original quantum states. These disturbances will be detected during the first eavesdropping check. Furthermore, since Eve has no knowledge of the key value , she cannot correctly identify or distinguish the information particle sequences corresponding to those particles. Consequently, Eve is unable to obtain Alice’s secret message . Moreover, Eve attempts to compare the measurement results of and in an effort to identify the positions corresponding to the information particle sequence. However, after encoding, Bob rearranges the order of the information particles and decoy particles. Since Eve has no knowledge of , she cannot infer the rearrangement order. Consequently, she is unable to extract any useful information by comparing the measurement results of and , and therefore cannot obtain Bob’s secret message .
After the above analysis, our protocol can effectively resist the double CNOT attack.
4 Efficiency analysis and comparison
The efficiency formula [25] for a quantum protocol is defined as: , where denotes the number of secret bits successfully exchanged between the parties, represents the number of quantum qubits utilized (excluding those consumed for security checks), and indicates the number of classical bits publicly communicated to facilitate the secret exchange. In the proposed protocol, the number of secret bits mutually exchanged between Alice and Bob is . Alice uses qubits to encode her secret information. After measuring Alice’s secret information, Bob prepares qubits carrying his own secret information to replace Alice’s original qubits. Thus, the total number of quantum bits is . Since Alice and Bob do not disclose any information via a public channel that is relevant for mutual decryption, . The efficiency of this protocol is . We compared existing protocols with the proposed protocol, and the comparison results are summarized in Table 2. In the first row of the table, “Public” indicates whether the protocol discloses classical information for decryption purposes.
TABLE 2
| Protocol | Type | Quantum channel | Measured basis | Public | Efficient |
|---|---|---|---|---|---|
| [26] | QD | Hyperentangled bell state | Bell, HBell | Yes | 50% |
| [27] | QD | Two-particle product state | Z, X, bell | Yes | 40% |
| [15] | SQD | Single photon | Z, X | Yes | 66.7% |
| [16] | SQD | Bell state | Z, bell | Yes | 20% |
| [18] | SQD | Hyperentangled bell state | Z, HBell | Yes | <15.4% |
| [19] | SQD | GHZ state | Z, GHZ | Yes | <16.7% |
| [20] | SQD | Four-particle Ω state | Z, Three-bit joint | Yes | 55.6% |
| Our | SQD | Single photon | Z, X | No | 100% |
Comparison with existing protocols.
As summarized in Table 2, the proposed protocol exhibits clear advantages over existing full quantum dialogue protocols by substantially reducing the implementation burden on the semi-quantum party. Compared with representative semi-quantum protocols, our protocol requires a more easily realizable quantum channel, while the full-quantum party performs only single-qubit measurements, thereby lowering experimental complexity. In addition, no classical information related to decryption is disclosed during the protocol execution, which strengthens security and enhances overall communication efficiency. Consequently, the proposed protocol achieves superior efficiency relative to previously reported quantum dialogue protocols.
5 Conclusion
In summary, we propose an efficient semi-quantum dialogue protocol that employs single photons as quantum channels. During the initialization stage, the two communicating parties share a one-time random bit string, and then both parties securely encode and exchange messages through single photons. Finally, both parties can exchange their secret information securely. Security analysis shows that the protocol effectively resists common quantum attacks without information leakage. Moreover, compared with the existing SQD protocols, our protocol offers high security, improved efficiency, and better practical feasibility.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
J-TC: Writing – original draft. J-YL: Writing – original draft. X-JX: Writing – review and editing. C-YL: Writing – review and editing. F-GL: Writing – review and editing. LZ: Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This research was supported by the National Natural Science Foundation of China (62272090), the Project of Science and Technology Tackling Key Problems in Henan Province (Grant nos 252102210178, 252102110182, 252102211105, 262102210208, and 262102210202), the Key Laboratory of Innovation and Testing Verification for Cryptographic Application Technology, Ministry of Industry and Information Technology (Grant no. MMCXKT-2025-24), and Postgraduate Education Reform and Quality Improvement Project of Henan Province (YJS2025ZX10).
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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Summary
Keywords
decoy particle, information entropy, quantum communication efficiency, semi-quantum dialogue, single photons
Citation
Cui J-T, Liu J-Y, Xin X-J, Li C-Y, Li F-G and Zhang L (2026) Efficient semi-quantum dialogue protocol using single-photon. Front. Phys. 14:1806357. doi: 10.3389/fphy.2026.1806357
Received
07 February 2026
Revised
04 March 2026
Accepted
10 March 2026
Published
23 March 2026
Volume
14 - 2026
Edited by
Q. H. Liu, Hunan University, China
Reviewed by
Tian Yuan, Beijing University of Posts and Telecommunications (BUPT), China
Chongqiang Ye, Hangzhou City University, China
Updates
Copyright
© 2026 Cui, Liu, Xin, Li, Li and Zhang.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Jun-Yao Liu, 332416010926@zzuli.edu.cn
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.