Mark M. Wilde, Patrick Hayden, Francesco Buscemi, Min-Hsiu Hsieh
Winter's measurement compression theorem stands as one of the most penetrating insights of quantum information theory. In addition to making an original and profound statement about measurement in quantum theory, it also underlies several other general protocols used for entanglement distillation or local purity distillation. The theorem provides for an asymptotic decomposition of any quantum measurement into an "extrinsic" source of noise (classical noise in the measurement that does not convey information) and "intrinsic" quantum noise that can be due in part to the nonorthogonality of quantum states. This decomposition leads to an optimal protocol for having a sender simulate many independent instances of a quantum measurement and send the measurement outcomes to a receiver, using as little communication as possible. The protocol assumes that the parties have access to some amount of common randomness, which is a strictly weaker resource than classical communication. In this paper, we provide a full review of Winter's measurement compression theorem. We then prove an extension of this theorem to the case in which the sender is not required to receive the outcomes of the simulated measurement. The total cost of common randomness and classical communication can be lower for such a "non-feedback" simulation, and we prove a single-letter converse theorem demonstrating optimality. We then review the Devetak-Winter theorem on classical data compression with quantum side information, providing new proofs of its achievability and converse parts. From there, we outline a new protocol that we call "measurement compression with quantum side information." Finally, we prove a single-letter theorem characterizing measurement compression with quantum side information when the sender is not required to obtain the measurement outcome.
View original:
http://arxiv.org/abs/1206.4121
No comments:
Post a Comment