Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Axioms

Two-Party Quantum Private Comparison with Pauli Operators

Min Hou, Yue Wu, Shibin Zhang

Published Jul 22, 2025• 2 citations
Publisher

Abstract

Quantum private comparison (QPC) is a quantum cryptographic protocol designed to enable two mutually distrustful parties to securely compare sensitive data without disclosing their private information to each other or any external entities. This study proposes a novel QPC protocol that leverages Bell states to ensure data privacy, utilizing the fundamental principles of quantum mechanics. Within this framework, two participants, each possessing a secret integer, encode the binary representation of their values using Pauli-X and Pauli-Z operators applied to quantum states transmitted from a semi-honest third party (TP). The TP, which is bound to protocol compliance and prohibited from colluding with either participant, measures the received sequences to determine the comparison result without accessing the participants’ original inputs. Theoretical analyses and simulations validate the protocol’s strong security, high efficiency, and practical feasibility in quantum computing environments. An advantage of the proposed protocol lies in its optimized utilization of Bell states, which enhances qubit efficiency and experimental practicality. Moreover, the proposed protocol outperforms several existing Bell-state-based QPC schemes in terms of efficiency.

DOI
10.3390/axioms14080549

Related papers

New Quantum Private Comparison Using Bell States

Min Hou, Yue Wu

Quantum private comparison (QPC) represents a cryptographic approach that enables two parties to determine whether their confidential data are equivalent, without disclosing the actual values. Most existing QPC protocols utilizing single photons or Bell states are considered highly feasible, but they suffer from inefficiency. To address this issue, we present a novel QPC protocol that capitalizes on the entanglement property of Bell states and local operations to meet the requirements of efficiency. In the proposed protocol, two participants with private inputs perform local operations on shared Bell states received from a semi-honest third party (STP). Afterward, the modified qubits are returned to the STP, who can then determine the equality of the private inputs and relay the results to the participants. A simulation on the IBM Quantum Cloud Platform confirmed the feasibility of our protocol, and a security analysis further demonstrated that the STP and both participants were unable to learn anything about the individual private inputs. In comparison to other QPC protocols, our proposed solution offers superior performance in terms of efficiency.

Entropy•Aug 13, 2024•20 citations

Quantum Private Comparison Protocol with Cluster States

Min Hou, Yue Wu

In this paper, we introduce a quantum private comparison (QPC) protocol designed for two players to securely and privately assess the equality of their private information. The protocol utilizes four-particle cluster states prepared by a semi-honest third party (TP), who strictly adheres to the protocol without deviation or collusion with any participant. The TP facilitates the private comparison by enabling users to encode their information through bit-flip or phase-shift operators applied to the received quantum sequences. Once the information is encoded, the sequences are returned to the TP, who can derive the comparison results without accessing any details of the private information. This design ensures correctness, privacy, and fairness throughout the process. The QPC protocol is robust against both external threats and participant attacks due to the incorporation of the decoy-state method and quantum key distribution techniques. Additionally, the protocol employs unitary operations and Bell-basis measurements, enhancing its technical feasibility for practical implementation. Notably, the proposed protocol achieves a qubit efficiency of up to 50%. This efficiency, combined with its strong security features, establishes the QPC protocol as a promising solution for private information comparisons within the realm of quantum cryptography.

Axioms•Jan 19, 2025•6 citations

Two-Party Quantum Private Comparison Protocol Based on Rotational Encryption

Min Hou, Yue Wu

In this paper, we introduce a two-party quantum private comparison (QPC) protocol that employs single photons as quantum resources and utilizes rotational encryption to safeguard the privacy of the inputs. This protocol enables two parties to compare their private data without disclosing any information beyond the outcome of the comparison. The participants’ private data are encoded as single photons, which are encrypted using a rotational encryption method. These encrypted single photons are then transmitted to a semi-honest third party (TP), who conducts single-particle measurements to determine if the users’ private data are equal and subsequently announces the results to the participants. By harnessing the principles of quantum mechanics, we ensure robust protection against potential eavesdropping and participant attacks. In contrast to numerous existing QPC protocols that rely on multi-qubit or d-dimensional quantum states, our method exhibits superior efficiency and practicality. Specifically, our protocol achieves a qubit efficiency of 50% by using two single photons to compare one bit of classical information, and single photons are easier to prepare than multi-qubit and d-dimensional quantum states.

Applied Sciences•Jan 13, 2025•3 citations

Efficient Quantum Private Comparison with Unitary Operations

Min Hou, Yue Wu

Quantum private comparison (QPC) is a crucial component of quantum multiparty computing (QMPC), allowing parties to compare their private inputs while ensuring that no sensitive information is disclosed. Many existing QPC protocols that utilize Bell states encounter efficiency challenges. In this paper, we present a novel and efficient QPC protocol that capitalizes on the distinct characteristics of Bell states to enable secure comparisons. Our method transforms private inputs into unitary operations on shared Bell states, which are then returned to a third party to obtain the comparison results. This approach enhances efficiency and decreases the reliance on complex quantum resources. A single Bell state can compare two classical bits, achieving a qubit efficiency of 100%. We illustrate the feasibility of the protocol through a simulation on the IBM Quantum Cloud Platform. The security analysis confirms that our protocol is resistant to both eavesdropping and attacks from participants.

Mathematics•Nov 13, 2024•14 citations

Two-Party Quantum Private Comparison Protocol for Direct Secret Comparison

Min Hou, Yue Wu

In this paper, we leverage the properties of the swap test to evaluate the similarity of two qubits and propose a two-party quantum private comparison (QPC) protocol involving a semi-trusted third party (TP). The TP facilitates the comparison between participants without accessing their private information, other than the final comparison results. Our protocol encodes participants’ secret integers directly into the amplitudes of single-photon states and introduces a novel method for secret-to-secret comparison rather than the traditional bit-to-bit comparison, resulting in improved scalability. To ensure security, the encoded single-photon states are concealed using rotation operations. The comparison results are derived through the implementation of the swap test. A simulation on the IBM Quantum Platform demonstrates the protocol’s feasibility, and a security analysis confirms its robustness against potential eavesdropping and participant attacks. Compared with existing QPC protocols that employ bit-to-bit comparison methods, our approach offers improved practicality and scalability. Specifically, it integrates single-photon states, rotation operations, and the swap test as key components for direct secret comparison, facilitating easier implementation with quantum technology.

Mathematics•Jan 20, 2025•5 citations

New Quantum Private Comparison Using Four-Particle Cluster State

Min Hou, Yue Wu, Shibin Zhang

Quantum private comparison (QPC) enables two users to securely conduct private comparisons in a network characterized by mutual distrust while guaranteeing the confidentiality of their private inputs. Most previous QPC protocols were primarily used to determine the equality of private information between two users, which constrained their scalability. In this paper, we propose a QPC protocol that leverages the entanglement correlation between particles in a four-particle cluster state. This protocol can compare the information of two groups of users within one protocol execution, with each group consisting of two users. A semi-honest third party (TP), who will not deviate from the protocol execution or conspire with any participant, is involved in assisting users to achieve private comparisons. Users encode their inputs into specific angles of rotational operations performed on the received quantum sequence, which is then sent back to TP. Security analysis shows that both external attacks and insider threats are ineffective at stealing private data. Finally, we compare our protocol with some previously proposed QPC protocols.

Entropy•Jun 14, 2024•11 citations
Quantum private comparison (QPC) is a quantum cryptographic protocol designed to enable two mutually distrustful parties to securely compare sensitive data without disclosing their private information to each other or any external entities. This study proposes a novel QPC protocol that leverages Bell states to ensure data privacy, utilizing the fundamental principles of quantum mechanics. Within this framework, two participants, each possessing a secret integer, encode the binary representation of their values using Pauli-X and Pauli-Z operators applied to quantum states transmitted from a semi-honest third party (TP). The TP, which is bound to protocol compliance and prohibited from colluding with either participant, measures the received sequences to determine the comparison result without accessing the participants’ original inputs. Theoretical analyses and simulations validate the protocol’s strong security, high efficiency, and practical feasibility in quantum computing environments. An advantage of the proposed protocol lies in its optimized utilization of Bell states, which enhances qubit efficiency and experimental practicality. Moreover, the proposed protocol outperforms several existing Bell-state-based QPC schemes in terms of efficiency.
Quantum private comparison (QPC) represents a cryptographic approach that enables two parties to determine whether their confidential data are equivalent, without disclosing the actual values. Most existing QPC protocols utilizing single photons or Bell states are considered highly feasible, but they suffer from inefficiency. To address this issue, we present a novel QPC protocol that capitalizes on the entanglement property of Bell states and local operations to meet the requirements of efficiency. In the proposed protocol, two participants with private inputs perform local operations on shared Bell states received from a semi-honest third party (STP). Afterward, the modified qubits are returned to the STP, who can then determine the equality of the private inputs and relay the results to the participants. A simulation on the IBM Quantum Cloud Platform confirmed the feasibility of our protocol, and a security analysis further demonstrated that the STP and both participants were unable to learn anything about the individual private inputs. In comparison to other QPC protocols, our proposed solution offers superior performance in terms of efficiency.
In this paper, we introduce a quantum private comparison (QPC) protocol designed for two players to securely and privately assess the equality of their private information. The protocol utilizes four-particle cluster states prepared by a semi-honest third party (TP), who strictly adheres to the protocol without deviation or collusion with any participant. The TP facilitates the private comparison by enabling users to encode their information through bit-flip or phase-shift operators applied to the received quantum sequences. Once the information is encoded, the sequences are returned to the TP, who can derive the comparison results without accessing any details of the private information. This design ensures correctness, privacy, and fairness throughout the process. The QPC protocol is robust against both external threats and participant attacks due to the incorporation of the decoy-state method and quantum key distribution techniques. Additionally, the protocol employs unitary operations and Bell-basis measurements, enhancing its technical feasibility for practical implementation. Notably, the proposed protocol achieves a qubit efficiency of up to 50%. This efficiency, combined with its strong security features, establishes the QPC protocol as a promising solution for private information comparisons within the realm of quantum cryptography.
In this paper, we introduce a two-party quantum private comparison (QPC) protocol that employs single photons as quantum resources and utilizes rotational encryption to safeguard the privacy of the inputs. This protocol enables two parties to compare their private data without disclosing any information beyond the outcome of the comparison. The participants’ private data are encoded as single photons, which are encrypted using a rotational encryption method. These encrypted single photons are then transmitted to a semi-honest third party (TP), who conducts single-particle measurements to determine if the users’ private data are equal and subsequently announces the results to the participants. By harnessing the principles of quantum mechanics, we ensure robust protection against potential eavesdropping and participant attacks. In contrast to numerous existing QPC protocols that rely on multi-qubit or d-dimensional quantum states, our method exhibits superior efficiency and practicality. Specifically, our protocol achieves a qubit efficiency of 50% by using two single photons to compare one bit of classical information, and single photons are easier to prepare than multi-qubit and d-dimensional quantum states.
Quantum private comparison (QPC) is a crucial component of quantum multiparty computing (QMPC), allowing parties to compare their private inputs while ensuring that no sensitive information is disclosed. Many existing QPC protocols that utilize Bell states encounter efficiency challenges. In this paper, we present a novel and efficient QPC protocol that capitalizes on the distinct characteristics of Bell states to enable secure comparisons. Our method transforms private inputs into unitary operations on shared Bell states, which are then returned to a third party to obtain the comparison results. This approach enhances efficiency and decreases the reliance on complex quantum resources. A single Bell state can compare two classical bits, achieving a qubit efficiency of 100%. We illustrate the feasibility of the protocol through a simulation on the IBM Quantum Cloud Platform. The security analysis confirms that our protocol is resistant to both eavesdropping and attacks from participants.
In this paper, we leverage the properties of the swap test to evaluate the similarity of two qubits and propose a two-party quantum private comparison (QPC) protocol involving a semi-trusted third party (TP). The TP facilitates the comparison between participants without accessing their private information, other than the final comparison results. Our protocol encodes participants’ secret integers directly into the amplitudes of single-photon states and introduces a novel method for secret-to-secret comparison rather than the traditional bit-to-bit comparison, resulting in improved scalability. To ensure security, the encoded single-photon states are concealed using rotation operations. The comparison results are derived through the implementation of the swap test. A simulation on the IBM Quantum Platform demonstrates the protocol’s feasibility, and a security analysis confirms its robustness against potential eavesdropping and participant attacks. Compared with existing QPC protocols that employ bit-to-bit comparison methods, our approach offers improved practicality and scalability. Specifically, it integrates single-photon states, rotation operations, and the swap test as key components for direct secret comparison, facilitating easier implementation with quantum technology.
Quantum private comparison (QPC) enables two users to securely conduct private comparisons in a network characterized by mutual distrust while guaranteeing the confidentiality of their private inputs. Most previous QPC protocols were primarily used to determine the equality of private information between two users, which constrained their scalability. In this paper, we propose a QPC protocol that leverages the entanglement correlation between particles in a four-particle cluster state. This protocol can compare the information of two groups of users within one protocol execution, with each group consisting of two users. A semi-honest third party (TP), who will not deviate from the protocol execution or conspire with any participant, is involved in assisting users to achieve private comparisons. Users encode their inputs into specific angles of rotational operations performed on the received quantum sequence, which is then sent back to TP. Security analysis shows that both external attacks and insider threats are ineffective at stealing private data. Finally, we compare our protocol with some previously proposed QPC protocols.