The paper "Quantum Fingerprinting" by Buhrman, Cleve, Watrous, and de Wolf explores the concept of quantum fingerprinting, which is a method to associate a shorter quantum fingerprint with each string such that two distinct strings can be distinguished with high probability. Unlike classical fingerprinting, where fingerprints can be exponentially smaller than the original strings if parties share a random key, quantum fingerprinting does not require shared keys or entanglement. The authors present a scheme where quantum fingerprints are exponentially shorter than the original strings and provide a test to distinguish between any two unknown quantum fingerprints with high probability. This scheme implies an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity. The paper also discusses the optimality of the fingerprinting methods and the efficiency of the distinguishing tests. Additionally, it considers the use of a shared quantum key, showing that exact fingerprinting can be achieved with significantly fewer qubits compared to classical fingerprinting.The paper "Quantum Fingerprinting" by Buhrman, Cleve, Watrous, and de Wolf explores the concept of quantum fingerprinting, which is a method to associate a shorter quantum fingerprint with each string such that two distinct strings can be distinguished with high probability. Unlike classical fingerprinting, where fingerprints can be exponentially smaller than the original strings if parties share a random key, quantum fingerprinting does not require shared keys or entanglement. The authors present a scheme where quantum fingerprints are exponentially shorter than the original strings and provide a test to distinguish between any two unknown quantum fingerprints with high probability. This scheme implies an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity. The paper also discusses the optimality of the fingerprinting methods and the efficiency of the distinguishing tests. Additionally, it considers the use of a shared quantum key, showing that exact fingerprinting can be achieved with significantly fewer qubits compared to classical fingerprinting.