Tight Bounds on the Accessible Information and the Informational Power

Abstract

The accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states. Analogously, the informational power quantifies the amount of classical information that can be extracted by a quantum measurement. For both quantities, we provide upper and lower bounds that depend only on the dimension of the system, and we prove their tightness. In the case of symmetric informationally complete (SIC) ensembles and measurements, stronger bounds are provided and their tightness proved for qubits and qutrits. From our upper bounds, we notice, perhaps surprisingly, that the statistics generated by SIC ensembles or measurements in arbitrary dimension, though optimal for tomographic purposes, in fact never contains more than just one bit of information, the rest being constituted by completely random bits. On the other hand, from our lower bounds, we obtain an explicit strategy beating the so-called "pretty-good" one for the extraction of mutual information in the case of SIC ensembles and measurements.

9 pages, 1 figure, updated references, published version

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• Device-independent tests of quantum measurements
• Maximally informative ensembles for SIC-POVMs in dimension 3
• On the Brukner-Zeilinger approach to information in quantum measurements
• Accessible Information and Informational Power of Quantum 2-designs
• A complete and operational resource theory of measurement sharpness
• Hierarchy of Bounds on Accessible Information and Informational Power
• Communication capacity of mixed quantum t designs
• Discrimination power of a quantum detector
• Tradeoff relations between accessible information, informational power, and purity