We present a quantum logic scheme to detect atomic and molecular ions in different states of angular momentum based on their magnetic g-factors. The state-dependent magnetic g-factors mean that electronic, rotational or hyperfine states may be distinguished by their Zeeman splittings in a given magnetic field. Driving motional sidebands of a chosen Zeeman splitting enables reading out the corresponding state of angular momentum with an auxillary logic ion. As a proof-of-principle demonstration,

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... we show that we can detect the ground electronic state of a ^174Yb^+ ion using ^171Yb^+ as the logic ion. Further, we can distinguish between the ^174Yb^+ ion being in its ground electronic state versus the metastable ^2D_3/2 state. We discuss the suitability of this scheme for the detection of rotational states in molecular ions.