Abstract:

We provide new results for computing and comparing the quantum gate fidelity of quantum channels via their Choi matrices. We extend recent work that showed there exist non-dual pairs of quantum channels with equal gate fidelity by providing an explicit characterization of all such channels. We use our characterization to show that when the dimension is 2 (or 3, under slightly stronger hypotheses), the gate fidelity of two channels is equal if and only if their difference equals the difference of some unital map and its dual – a fact that has been shown to be false when the dimension is 4 or larger. We also present a formula for the minimum gate fidelity of a channel in terms of a well-studied norm on a compression of its Choi matrix. As a consequence, several new ways of bounding and approximating the minimum gate fidelity follow, including a simple semidefinite program to compute it for qubit channels.

Authors:

• Nathaniel Johnston
• David Kribs

Download:

• Official publication in Journal of Physics A: Mathematical and Theoretical
• Preprint from arXiv:1102.0948 [quant-ph]
• Local preprint [pdf]
• Slideshow presentation [pdf]

Status:

• Published in Journal of Physics A: Mathematical and Theoretical

Cite as:

• N. Johnston and D. W. Kribs, Quantum Gate Fidelity in Terms of Choi Matrices. Journal of Physics A: Mathematical and Theoretical 44, 495303 (2011).

Supplementary Material:

• Theorem 7 worksheets – two Maple 8 worksheets that help work through the messy algebra in Theorem 7