Quantum error correction and generalized numerical ranges

Details Quantum error correction and generalized numerical ranges Quantum error correction and generalized numerical ranges

2008-12-27

arxiv.org/abs/0812.4772v1

Mathematics

Functional Analysis

15 pages

Scientific paper

For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint higher rank numerical ranges are obtained and their implications to quantum computing are discussed. It is shown that if the dimension of the underlying Hilbert space of the quantum states is sufficiently large, the joint higher rank numerical range of operators is always star-shaped and contains a non-empty convex subset. In case the operators are infinite dimensional, the joint infinite rank numerical range of the operators is a convex set closely related to the joint essential numerical ranges of the operators.

Affiliated with

Also associated with

No associations

Rating

Quantum error correction and generalized numerical ranges 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 Quantum error correction and generalized numerical ranges, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum error correction and generalized numerical ranges will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-478096