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This work proposes a $d$-dimensional quantum multi-secret sharing scheme witha cheat detection mechanism. The dealer creates multiple secrets anddistributes the shares of these secrets using multi-access structures and amonotone span program. The dealer detects the cheating of each participantusing the Black box's cheat detection mechanism. To detect the participants'deceit, the dealer distributes secret shares' shadows derived from a randomlyinvertible matrix $X$ to the participants, stored in the black box. The Blackbox identifies the participant's deceitful behavior during the secret recoveryphase. Only honest participants authenticated by the Black box acquire theirsecret shares to recover the multiple secrets. After the Black box cheatingverification, the participants reconstruct the secrets by utilizing the unitaryoperations and quantum Fourier transform. The proposed protocol is reliable inpreventing attacks from eavesdroppers and participants. The scheme's efficiencyis demonstrated in different noise environments: dit-flip noise, $d$-phase-flipnoise, and amplitude-damping noise, indicating its robustness in practicalscenarios. The proposed protocol provides greater versatility, security, andpracticality.

Quantum multi-secret sharing scheme with access structures and cheat identification