The paper introduces sufficient real positive maps and shows that minimal sufficient real Jordan algebras are generated by the likelihood-ratio set together with the projected reference state.
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Quantum Sufficiency for Self-Adjoint Statistical Models via Likelihood-Type Operators on Real $*$-Subalgebras and Real Jordan Algebras
The paper introduces sufficient real positive maps and shows that minimal sufficient real Jordan algebras are generated by the likelihood-ratio set together with the projected reference state.