On the role of entanglement in quantum-computational speed-up

@article{Jozsa2003OnTR,
  title={On the role of entanglement in quantum-computational speed-up},
  author={Richard Jozsa and Noah Linden},
  journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
  year={2003},
  volume={459},
  pages={2011 - 2032}
}
  • R. Jozsa, N. Linden
  • Published 30 January 2002
  • Physics, Computer Science
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
For any quantum algorithm operating on pure states, we prove that the presence of multi‐partite entanglement, with a number of parties that increases unboundedly with input size, is necessary if the quantum algorithm is to offer an exponential speed‐up over classical computation. Furthermore, we prove that the algorithm can be efficiently simulated classically to within a prescribed tolerance η even if a suitably small amount of global entanglement is present. We explicitly identify the… 
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