Privacy and Interaction in Quantum Communication Complexity and a Theorem about the Relative Entropy of Quantum States

@inproceedings{Jain2002PrivacyAI,
  title={Privacy and Interaction in Quantum Communication Complexity and a Theorem about the Relative Entropy of Quantum States},
  author={Rahul Jain and Jaikumar Radhakrishnan and Pranab Sen},
  booktitle={FOCS},
  year={2002}
}
We prove a theorem about the relative entropy of quantum states, which roughly states that if the relative entropy, S(ρ‖σ) ∆ = Tr ρ(log ρ− log σ), of two quantum states ρ and σ is at mostc, thenρ/2 ‘sits inside’ σ. Using this ‘substate’ theorem, we give tight lower bounds for the privacy loss of bounded error quantum communication protocols for the index function problem. We also give tight lower bounds for the k-round bounded error quantum communication complexity of the pointer chasing… CONTINUE READING