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Absolute Dimensionality of Quantum Ensembles.

Alexander Bernal1, Gabriele Cobucci2, Martin J Renner3,4

  • 1Instituto de Física Teórica, IFT-UAM/CSIC, <a href="https://ror.org/01cby8j38">Universidad Autónoma de Madrid</a>, Cantoblanco, 28049 Madrid, Spain.

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This summary is machine-generated.

We introduce a new, basis-independent measure for quantum state dimensionality. This absolute dimension determines if a quantum ensemble can be simulated in lower-dimensional spaces, advancing quantum information processing.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Physics

Background:

  • Traditional quantum state dimension is basis-dependent.
  • A basis-independent measure is needed for robust quantum information processing.

Purpose of the Study:

  • To propose an absolute, basis-independent notion of dimensionality for quantum ensembles.
  • To develop criteria for determining this absolute dimension.
  • To explore its implications for quantum information processing.

Main Methods:

  • Introduced a simulation-based definition of absolute dimensionality.
  • Developed analytical witness criteria.
  • Utilized semidefinite programming based on information capacity.
  • Constructed simulation models for noisy pure quantum states.

Main Results:

  • Established a basis-independent measure for quantum ensemble dimensionality.
  • Provided analytical and semidefinite programming criteria for its determination.
  • Demonstrated simulation models for pure quantum states under white noise, proving optimality in certain cases.
  • Developed efficient numerical methods for generic ensembles.

Conclusions:

  • The proposed absolute dimensionality offers a fundamental characterization of quantum ensembles.
  • This concept is crucial for understanding and advancing high-dimensional quantum information processing.
  • The developed methods provide practical tools for analyzing quantum state complexity.