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Amplification, Inference, and the Manifestation of Objective Classical Information.

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Summary

This study introduces a new Holevo quantity for quantifying classical information accessible in quantum systems. This quantity provides a tighter bound than traditional methods, especially under decoherence, offering a universal approach to information quantification.

Keywords:
Holevoamplificationdecoherenceinferencequantum Chernoff boundquantum Darwinismquantum-to-classical transition

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Area of Science:

  • Quantum Information Theory
  • Environmental Interactions
  • Information Measurement

Background:

  • Objective information in everyday reality is shaped by environmental interactions with quantum systems.
  • Quantum mutual information and the Holevo quantity are standard measures for correlations between quantum systems and environmental fragments.
  • Previous work quantified information transmittable via quantum channels using these measures.

Purpose of the Study:

  • To examine a novel Holevo quantity derived from a quantum-classical state (quantum system S to measured environment fragment F).
  • To demonstrate that this new quantity offers an upper bound for accessible classical information about S in F.
  • To show this bound can be tighter than the conventional Holevo quantity.

Main Methods:

  • Analysis of a quantum-classical state (quantum S to measured F).
  • Comparison of the novel Holevo quantity with the traditional Holevo quantity.
  • Investigation under conditions of good decoherence, where the environment measures pointer states of S.

Main Results:

  • The novel Holevo quantity provides a tighter upper bound on accessible classical information about S in F.
  • Under good decoherence, this bound equals the accessible information.
  • The accessible information correlates with optimal detection error probability, mirroring the quantum Chernoff bound's behavior.

Conclusions:

  • The examined Holevo quantity offers a more refined measure of accessible classical information from quantum systems.
  • This approach, particularly under decoherence, aligns with the quantum Chernoff bound, providing a universal, single-shot framework.
  • It quantifies records of missing classical information about the quantum system S.