2017/12/08 by Benjamin Lovitz, Norbert Lütkenhaus · 7 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer network #Computer science #Discrete mathematics #Information leakage #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Qubit #Realization (probability) #Statistics #Tensor product #quant-ph
paper · pdf · doi:10.1103/physreva.97.032340
published in Physical Review A 97(3) (American Physical Society) · 14 pages, 3 figures
arxiv created 2017/12/08 · openalex publication_date 2018/03/28 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce several families of quantum fingerprinting protocols to evaluate the equality function on two n-bit strings in the simultaneous message passing model. The original quantum fingerprinting protocol uses a tensor product of a small number of O(logn)-qubit high-dimensional signals [H. Buhrman et al., Phys. Rev. Lett. 87, 167902 (2001)], whereas a recently proposed optical protocol uses a tensor product of O(n) single-qubit signals, while maintaining the O(logn) information leakage of the original protocol [J. M. Arazola and N. L"utkenhaus, Phys. Rev. A 89, 062305 (2014)]. We find a family of protocols which interpolate between the original and optical protocols while maintaining the O(logn) information leakage, thus demonstrating a tradeoff between the number of signals sent and the dimension of each signal. There has been interest in experimental realization of the recently proposed optical protocol using coherent states [F. Xu et al., Nat. Commun. 6, 8735 (2015); J.-Y. Guan et al., Phys. Rev. Lett. 116, 240502 (2016)], but as the required number of laser pulses grows linearly with the input size n, eventual challenges for the long-time stability of experimental setups arise. We find a coherent state protocol which reduces the number of signals by a factor (1)/(2) while also reducing the information leakage. Our reduction makes use of a simple modulation scheme in optical phase space, and we find that more complex modulation schemes are not advantageous. Using a similar technique, we improve a recently proposed coherent state protocol for evaluating the Euclidean distance between two real unit vectors [N. Kumar et al., Phys. Rev. A 95, 032337 (2017)] by reducing the number of signals by a factor (1)/(2) and also reducing the information leakage.