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An Information Quantity in Pure State Models.

Fuyuhiko Tanaka1,2

  • 1Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan.

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|April 23, 2022
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Summary

We introduce "purely quantum information" to quantify uncertainty in quantum computing systems, even after accounting for classical noise. This new measure connects to facility location problems in mathematical research.

Keywords:
complex projective spacefacility location problemminimum entropyquantum information

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Area of Science:

  • Quantum Information Science
  • Quantum Computing Error Models
  • Operations Research

Background:

  • Quantum computing systems are susceptible to errors, often modeled parametrically.
  • Assessing information gain within these parametric models, considering residual uncertainty beyond classical fluctuations, is crucial.

Purpose of the Study:

  • To propose a novel information quantity,
  • purely quantum information
  • , to quantify the inherent uncertainty in quantum systems.
  • To establish an operational meaning for this quantity and explore its mathematical connections.

Main Methods:

  • Developing a theoretical framework for quantifying information in parametric quantum error models.
  • Defining
  • purely quantum information
  • as a measure of residual quantum uncertainty.
  • Investigating the relationship between purely quantum information and facility location problems on the unit sphere (for qubits) and complex projective spaces (for general systems).

Main Results:

  • Purely quantum information quantifies uncertainty remaining in a quantum system after accounting for classical fluctuations.
  • The qubit case reveals a connection to the facility location problem on the unit sphere.
  • The general case extends this to facility location problems in complex projective spaces.

Conclusions:

  • Purely quantum information provides a new metric for understanding quantum system uncertainty.
  • This quantity is operationally meaningful and links quantum information theory to established problems in operations research.
  • Purely quantum information is related to minimum entropy, offering an alternative perspective to von Neumann entropy.