Quantum Information Fusion and Correction under the Transferable Belief Model

The transferable belief model (TBM), developed within Dempster-Shafer theory, represents ambiguity and partial ignorance through set-valued belief masses. Its classical operations, however, can grow combinatorially over the power set. We formulate TBM reasoning on quantum circuits using the mass function quantum state (MFQS). The resulting framework covers belief representation, credal-level fusion and correction, product-space operations, and the generalized Bayesian theorem. For prepared MFQS inputs, CCR and the entire α-junction use element-wise gate modules whose logical counts are linear in the number of frame elements. These circuits avoid explicit operation-stage updates over all 2n focal-set coordinates. A noisy multi-domain classifier-fusion example further demonstrates interpretable source fusion and improved robustness to gate-control noise. The results establish Dempster-Shafer structures as a semantic layer for quantum information processing beyond singleton-probability representations.