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The notion of dually flatness is of central importance in information geometry. Nevertheless, little is known about dually flat structures on quantum statistical manifolds except that the Bogoliubov metric admits a global dually flat structure on a quantum state space    $${{\mathcal {S}}}({{\mathbb {C}}}^d)$$  S ( C d ) for any    $$d\ge 2$$  d ≥ 2 . In this paper, we show that every monotone metric on a two-level quantum state space    $${{\mathcal {S}}}({{\mathbb {C}}}^2)$$  S ( C 2 ) admits a local dually flat structure.

Dually flat structures induced from monotone metrics on a two-level quantum state space