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Algorithmic complexity and entanglement of quantum states.

Caterina E Mora1, Hans J Briegel

  • 1Institut für Quantenoptik und Quanteninformation der Osterreichischen Akademie der Wissenschaften, Innsbruck, Austria.

Physical Review Letters
|December 31, 2005
PubMed
Summary

We introduce a way to measure the algorithmic complexity of quantum states, providing upper bounds for different states. This research also links quantum entanglement to algorithmic complexity.

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Area of Science:

  • Quantum Information Science
  • Theoretical Computer Science
  • Quantum Computing

Background:

  • Algorithmic complexity is a fundamental concept in computer science, quantifying the resources needed for computation.
  • Quantum states possess unique properties that may be characterized by computational complexity.
  • Understanding the complexity of quantum states is crucial for advancing quantum information processing.

Purpose of the Study:

  • To define and quantify the algorithmic complexity of quantum states.
  • To establish upper bounds for the algorithmic complexity of specific quantum states.
  • To explore the relationship between quantum entanglement and algorithmic complexity.

Main Methods:

  • Development of a formal definition for the algorithmic complexity of a quantum state.
  • Calculation of upper bounds for algorithmic complexity across various classes of quantum states.
  • Mathematical analysis to establish a connection between entanglement measures and algorithmic complexity.

Main Results:

  • A precise definition for the algorithmic complexity of quantum states relative to a precision parameter.
  • Derived upper bounds for the algorithmic complexity of several example quantum states.
  • Demonstrated a direct correlation between the entanglement of a quantum state and its algorithmic complexity.

Conclusions:

  • Algorithmic complexity provides a novel lens for characterizing quantum states.
  • The established connection between entanglement and algorithmic complexity deepens our understanding of quantum information.
  • This framework has implications for quantum algorithm design and resource estimation.