Physics – Quantum Physics
Scientific paper
2010-10-09
Theory of Quantum Computation, Communication, and Cryptography, Lecture Notes in Computer Science, 2011, Volume 6519/2011, 9-2
Physics
Quantum Physics
19 pages, no figures, a new result added, published version to appear in Proceedings of TQC 2010
Scientific paper
10.1007/978-3-642-18073-6_2
This paper presents a series of results on the interplay between quantum estimation, cloning and finite de Finetti theorems. First, we consider the measure-and-prepare channel that uses optimal estimation to convert M copies into k approximate copies of an unknown pure state and we show that this channel is equal to a random loss of all but s particles followed by cloning from s to k copies. When the number k of output copies is large with respect to the number M of input copies the measure-and-prepare channel converges in diamond norm to the optimal universal cloning. In the opposite case, when M is large compared to k, the estimation becomes almost perfect and the measure-and-prepare channel converges in diamond norm to the partial trace over all but k systems. This result is then used to derive de Finetti-type results for quantum states and for symmetric broadcast channels, that is, channels that distribute quantum information to many receivers in a permutationally invariant fashion. Applications of the finite de Finetti theorem for symmetric broadcast channels include the derivation of diamond-norm bounds on the asymptotic convergence of quantum cloning to state estimation and the derivation of bounds on the amount of quantum information that can be jointly decoded by a group of k receivers at the output of a symmetric broadcast channel.
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