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An algorithm to explore entanglement in small systems.

R Reuvers1

  • 1Department of Applied Mathematics and Theoretical Physics (DAMTP), Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|July 7, 2018
PubMed
Summary

We developed a simple iterative algorithm using Schmidt decompositions to maximize quantum state entanglement norms. This method explores various quantum states and channel properties, optimizing entanglement across bipartite cuts.

Keywords:
Schmidt normsalgorithmentanglementfermionic reduced density matricesminimal output entropyvarieties of pure quantum states

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Entanglement

Background:

  • Quantifying entanglement in quantum states is crucial for understanding quantum systems.
  • Entanglement entropy and Schmidt norms are key measures of bipartite entanglement.
  • Existing methods for maximizing entanglement can be complex and computationally intensive.

Purpose of the Study:

  • To present a simple iterative algorithm for maximizing Schmidt norms of quantum states.
  • To explore the optimization of entanglement across multiple bipartite cuts simultaneously.
  • To investigate the application of this algorithm to diverse quantum information problems.

Main Methods:

  • Utilized Schmidt decompositions as the sole basis for the iterative algorithm.
  • Developed an iterative process to systematically maximize selected Schmidt norms.
  • Applied the algorithm to explore specific quantum states and channel properties.

Main Results:

  • The algorithm successfully maximizes or minimizes entanglement based on the chosen norm.
  • Demonstrated the ability to optimize entanglement across several bipartite cuts concurrently.
  • Showcased the algorithm's versatility in exploring topics like fermionic systems and absolutely maximally entangled states.

Conclusions:

  • The proposed iterative algorithm offers a straightforward approach to manipulating quantum entanglement.
  • The method provides a unified framework for studying various aspects of quantum entanglement.
  • Convergence is guaranteed, though success in finding the absolute maximum/minimum depends on the norm and subspace.