Sufficiency in quantum statistical inference
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This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in classical mathematical statistics. Sufficiency of a coarse-graining means that all information is extracted about the mutual relation of a given family of states. In the paper sufficient coarse-grainings are characterized in several equivalent ways and the non-commutative analogue of the factorization theorem is obtained. Among the applications the equality case for the strong subadditivity of the von Neumann entropy, the Imoto-Koashi theorem and exponential families are treated. The setting of the paper allows the underlying Hilbert space to be infinite dimensional.
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Cited by 3 Pith papers
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Quantum Sufficiency for Self-Adjoint Statistical Models via Likelihood-Type Operators on Real $*$-Subalgebras and Real Jordan Algebras
Quantum sufficiency for self-adjoint models is characterized via sufficient real positive maps on real Jordan algebras generated by likelihood-ratio sets, separating likelihood and modular aspects while admitting dege...
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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.
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Quantum Sufficiency for Self-Adjoint Statistical Models via Likelihood-Type Operators on Real $*$-Subalgebras and Real Jordan Algebras
Quantum sufficiency is reformulated on real *-subalgebras and Jordan algebras, with sufficient real positive maps, minimal sufficient structures characterized by likelihood-ratio sets, and Koashi-Imoto-type decomposit...
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