Quantum Gate Fidelity in Terms of Choi Matrices
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.
- Nathaniel Johnston
- David Kribs
- Official publication in Journal of Physics A: Mathematical and Theoretical
- Preprint from arXiv:1102.0948 [quant-ph]
- Local preprint [pdf]
- Slideshow presentation [pdf]
- Published in Journal of Physics A: Mathematical and Theoretical
- N. Johnston and D. W. Kribs, Quantum Gate Fidelity in Terms of Choi Matrices. Journal of Physics A: Mathematical and Theoretical 44, 495303 (2011).
- Theorem 7 worksheets – two Maple 8 worksheets that help work through the messy algebra in Theorem 7