A categorical semantics of quantum protocols

@article{Abramsky2004ACS,  title={A categorical semantics of quantum protocols},  author={Samson Abramsky and Bob Coecke},  journal={Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.},  year={2004},  pages={415-425},  url={https://api.semanticscholar.org/CorpusID:1980118}}
  • S. AbramskyB. Coecke
  • Published inProceedings of the 19th…18 February 2004
  • Physics, Computer Science
  • Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
This paper focuses on quantum information protocols, which exploit quantum-mechanical effects in an essential way and form the basis for novel and potentially very important applications to secure and fault-tolerant communication and computation.

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31 References

Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations

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