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Characterising the intersection of QMA and coQMA

par Massar, Serge ;Santha, Miklos
Référence Quantum Information Processing, 20, 12, 396
Publication Publié, 2021-12-01

Article révisé par les pairs

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Résumé :

We show that the functional analogue of QMA∩COQMA, denoted F(QMA∩COQMA), equals the complexity class Total Functional QMA (TFQMA). To prove this, we need to introduce an alternative definition of QMA∩COQMA in terms of a single quantum verification procedure. We show that if TFQMA equals the functional analogue of BQP (FBQP), then QMA∩COQMA=BQP. We show that if there is a QMA complete problem that (robustly) reduces to a problem in TFQMA , then QMA∩COQMA=QMA. Our results thus imply that if some of the inclusions between functional classes FBQP ⊆ TFQMA ⊆ FQMA are in fact equalities, then the corresponding inclusions in BQP⊆QMA∩COQMA⊆QMA are also equalities.