Sufficiency in quantum statistical inference

Abstract

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.

References in corpus (3)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Monotonicity of quantum relative entropy revisited
• Structure of sufficient quantum coarse-grainings

Cited by in corpus (53)

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• Divergence and Sufficiency for Convex Optimization
• Reversibility of a quantum channel: general conditions and their applications to Bosonic linear channels
• Quantum hypothesis testing and sufficient subalgebras
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• Explicit reconstruction of the entanglement wedge via the Petz map
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• Thermodynamically-Efficient Local Computation and the Inefficiency of Quantum Memory Compression
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• Quantum U-statistics
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• Markov property and strong additivity of von Neumann entropy for graded quantum systems
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• Quantum model reduction for continuous-time quantum filters
• Belavkin-Staszewski Quantum Markov Chains
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