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Scalable reconstruction of density matrices.

T Baumgratz1, D Gross, M Cramer

  • 1Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, 89069 Ulm, Germany.

Physical Review Letters
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Summary
This summary is machine-generated.

This study presents a scalable quantum state tomography method for reconstructing mixed states using matrix product operators. The technique relies on local information, making it efficient for large one-dimensional quantum systems.

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Area of Science:

  • Quantum Information Science
  • Quantum Many-Body Physics

Background:

  • Quantum state tomography (QST) is crucial for characterizing quantum systems.
  • Traditional QST faces challenges due to the exponential growth of Hilbert space with system size.
  • Efficient QST methods are needed for scalable quantum technologies.

Purpose of the Study:

  • To develop a scalable method for reconstructing mixed quantum states.
  • To leverage matrix product operators (MPOs) for efficient state reconstruction.
  • To demonstrate the feasibility of MPO-based QST using local measurements.

Main Methods:

  • Developed a reconstruction scheme based on matrix product operators (MPOs).
  • Utilized local information (local reductions) to determine MPOs.
  • Constructive proof showing MPOs are fully determined by local reductions.

Main Results:

  • A scalable method for quantum state tomography of mixed states approximated by MPOs.
  • The method requires only local information, enabling scalability with system size.
  • Successful application to both simulated and experimental ion trap data.

Conclusions:

  • Local information is sufficient to reconstruct MPO-represented quantum states.
  • This MPO-based approach offers a scalable solution for quantum state tomography.
  • The method has practical implications for characterizing complex quantum systems.