By using swap test, a quantum private comparison (QPC) protocol of arbitrary single qubit states with a semi-honest third party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she cannot conspire with any of participants. In the process of comparison, the TP cannot get two participants’ private information except the comparison results. According to the security analysis, the proposed protocol can resist both outsider attacks and participants’ attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, but it can compare two participants’ qubits by performing swap test, which is easier to implement with current technology. Meanwhile, the proposed protocol can compare secret integers. It encodes secret integers into the amplitude of quantum state rather than transfer them as binary representations, and the encoded quantum state is compared by performing the swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.By using swap test, a quantum private comparison (QPC) protocol of arbitrary single qubit states with a semi-honest third party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she cannot conspire with any of participants. In the process of comparison, the TP cannot get two participants’ private information except the comparison results. According to the security analysis, the proposed protocol can resist both outsider attacks and participants’ attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, but it can compare two participants’ qubits by performing swap test, which is easier to implement with current technology. Meanwhile, the proposed protocol can compare secret integers. It encodes secret integers into the amplitude of quantum state rather than transfer them as binary representations, and the encoded quantum state is compared by performing the swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.

Chinese Physics BDec 8, 202126 citations

Quantum multi-state Swap Test: an algorithm for estimating overlaps of arbitrary number quantum states

Wen Liu, Yang-Zhi Li, Han-Wen Yin +2 more

Abstract Estimating the overlap between two states is an important task with several applications in quantum information. However, the typical swap test circuit can only measure a sole pair of quantum states at a time. In this study, a recursive quantum circuit is designed to measure overlaps of n quantum states $\left | {\phi _{1} } \right \rangle ,\left | {\phi _{2} } \right \rangle ,\ldots\left | {\phi _{n} }\right \rangle $ | ϕ 1 〉 , | ϕ 2 〉 , … | ϕ n 〉 concurrently with $O(k2^{k})$ O ( k 2 k ) controlled-swap(CSWAP) gates and $O(k)$ O ( k ) ancillary qubits, where $k=\left \lceil {\log n} \right \rceil $ k = ⌈ log n ⌉ . All pairwise overlaps among input quantum states $|\langle \phi _{i}|\phi _{j}\rangle |^{2}$ | 〈 ϕ i | ϕ j 〉 | 2 can be obtained in this circuit. Compared with existing scheme for measuring the overlap of multiple quantum states, the circuit provides higher precision and less consumption of ancillary qubits. In addition, some simulation experiments are performed on IBM quantum cloud platform to verify the superiority of this algorithm.Abstract Estimating the overlap between two states is an important task with several applications in quantum information. However, the typical swap test circuit can only measure a sole pair of quantum states at a time. In this study, a recursive quantum circuit is designed to measure overlaps of n quantum states $\left | {\phi _{1} } \right \rangle ,\left | {\phi _{2} } \right \rangle ,\ldots\left | {\phi _{n} }\right \rangle $ | ϕ 1 〉 , | ϕ 2 〉 , … | ϕ n 〉 concurrently with $O(k2^{k})$ O ( k 2 k ) controlled-swap(CSWAP) gates and $O(k)$ O ( k ) ancillary qubits, where $k=\left \lceil {\log n} \right \rceil $ k = ⌈ log n ⌉ . All pairwise overlaps among input quantum states $|\langle \phi _{i}|\phi _{j}\rangle |^{2}$ | 〈 ϕ i | ϕ j 〉 | 2 can be obtained in this circuit. Compared with existing scheme for measuring the overlap of multiple quantum states, the circuit provides higher precision and less consumption of ancillary qubits. In addition, some simulation experiments are performed on IBM quantum cloud platform to verify the superiority of this algorithm.

EPJ Quantum TechnologyJul 25, 20243 citations

Quantum Hypothesis Testing and Discrimination of Quantum States

Springer eBooksSep 1, 20061 citation

A simple test for the separability of symmetric quantum states

Domenico D’Alessandro

Reports on Mathematical PhysicsAug 1, 20220 citations

O(k2^{k})

O ( k 2 k ) controlled-swap(CSWAP) gates and

O(k)

O ( k ) ancillary qubits, where $k=\left \lceil {\log n} \right \rceil $ k = ⌈ log n ⌉ . All pairwise overlaps among input quantum states

|\langle \phi _{i}|\phi _{j}\rangle |^{2}

| 〈 ϕ i | ϕ j 〉 | 2 can be obtained in this circuit. Compared with existing scheme for measuring the overlap of multiple quantum states, the circuit provides higher precision and less consumption of ancillary qubits. In addition, some simulation experiments are performed on IBM quantum cloud platform to verify the superiority of this algorithm.