Generalize convex-Gaussianity noise analysis beyond two-qubit parity-preserving gates
Develop generalizations of the Choi-state and concurrence method for arbitrary n-qubit unitary gates, arbitrary two-qubit channels, more general noise models, and resource theories beyond matchgate resourcefulness, including entanglement and spin coherence, and determine whether analogous efficiently tractable criteria exist for these resources.
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The method described in this paper is only applicable to 2-qubit parity preserving gates as only parity preserving gates will correspond to valid fermionic Choi states, and only 2-qubit gates will correspond to 4-mode Choi states with which the concurrence method applies. Further, we only characterize the resourcefulness of the combined gate and noise channel when it comes to resourcefulness in matchgate circuits. Therefore, future work may seek to generalize the method described here to arbitrary n-qubit unitary gates and to other resource theories. For instance, a PPT-like condition has recently been identified for fermions. This could include studying arbitrary two-qubit channels, replacing local depolarizing noise by more general noise models, and determining thresholds for resources such as entanglement or spin coherence; such thresholds could connect directly to applications including quantum networks and quantum sensing. One could ask whether criteria analogous to the concurrences used here exist that can be used to characterize other resources, and whether the computation thereof would similarly reduce to tractable calculation. These remain open and interesting directions.