Quantum fingerprinting.

@article{Buhrman2001QuantumF,
  title={Quantum fingerprinting.},
  author={Harry Buhrman and Richard Cleve and John Watrous and Ronald de Wolf},
  journal={Physical review letters},
  year={2001},
  volume={87 16},
  pages={
          167902
        },
  url={https://api.semanticscholar.org/CorpusID:1096490}
}
It is shown that fingerprints consisting of quantum information can be made exponentially smaller than the original strings without any correlations or entanglement between the parties, implying an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity.
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