Families of Quantum Fingerprinting Protocols

TL;DR

This paper introduces new families of quantum fingerprinting protocols that balance the number of signals and signal dimension, improving efficiency and reducing experimental challenges in quantum communication tasks.

Contribution

It presents a continuum of protocols interpolating between existing methods, and introduces a simple modulation scheme that halves the number of signals and information leakage.

Findings

Interpolated protocols maintain low information leakage

Reduced the number of signals in optical protocols by half

Improved protocols for Euclidean distance evaluation

Abstract

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 $\mathcal{O}(\log n)$-qubit high dimensional signals [Buhrman et al. 2001], whereas a recently-proposed optical protocol uses a tensor product of $\mathcal{O}(n)$ single-qubit signals, while maintaining the $\mathcal{O}(\log n)$ information leakage of the original protocol [Arrazola and L\"utkenhaus 2014]. We find a family of protocols which interpolate between the original and optical protocols while maintaining the $\mathcal{O}(\log n)$ information leakage, thus demonstrating a trade-off 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 [Xu et al. 2015, Guan et al. 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 set-ups 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 [Kumar et al. 2017] by reducing the number of signals by a factor $1/2$ and also reducing the information leakage.