On almost randomizing channels with a short Kraus decomposition

Details On almost randomizing channels with a short Kraus decomposition On almost randomizing channels with a short Kraus decomposition

2008-05-19

arxiv.org/abs/0805.2900v2

Mathematics

Probability

We added some background on geometry of Banach spaces

Scientific paper

10.1007/s00220-008-0695-y

For large d, we study quantum channels on C^d obtained by selecting randomly N independent Kraus operators according to a probability measure mu on the unitary group U(d). When mu is the Haar measure, we show that for N>d/epsilon^2$, such a channel is epsilon-randomizing with high probability, which means that it maps every state within distance epsilon/d (in operator norm) of the maximally mixed state. This slightly improves on a result by Hayden, Leung, Shor and Winter by optimizing their discretization argument. Moreover, for general mu, we obtain a epsilon-randomizing channel provided N > d (\log d)^6/epsilon^2$. For d=2^k (k qubits), this includes Kraus operators obtained by tensoring k random Pauli matrices. The proof uses recent results on empirical processes in Banach spaces.

Affiliated with

Also associated with

No associations

Rating

On almost randomizing channels with a short Kraus decomposition does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On almost randomizing channels with a short Kraus decomposition, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On almost randomizing channels with a short Kraus decomposition will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-648434