Reflected multi-entropy and its holographic dual

We introduce a mixed-state generalization of the multi-entropy through the canonical purification, which we call reflected multi-entropy. We propose the holographic dual of this measure. For the tripartite case, a field-theoretical calculation is performed using a six-point function of twist operators at large $c$ limit. At both zero and finite temperature, the field-theoretical results match the holographic results, supporting our holographic conjecture of this new measure.