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Systematic errors in current quantum state tomography tools.

Christian Schwemmer1, Lukas Knips1, Daniel Richart1

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany and Department für Physik, Ludwig-Maximilians-Universität, D-80797 München, Germany.

Physical Review Letters
|March 14, 2015
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Summary
This summary is machine-generated.

Common quantum state tomography methods cause errors, underestimating fidelity and overestimating entanglement. Linear data evaluation or measurement operator linearization provides reliable estimates and error bounds, avoiding these systematic biases.

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Area of Science:

  • Quantum Information Science
  • Experimental Quantum Physics
  • Quantum State Tomography

Background:

  • Quantum state tomography (QST) is crucial for characterizing quantum systems.
  • Standard QST methods often rely on optimization techniques like maximum likelihood or least squares.
  • These common methods can introduce systematic errors in estimating physical density matrices.

Purpose of the Study:

  • To identify and analyze systematic errors in common QST tools.
  • To propose alternative methods for obtaining accurate physical density matrices.
  • To develop reliable error bounds for quantum state estimation.

Main Methods:

  • Analysis of systematic errors in maximum likelihood and least squares optimization for QST.
  • Development and application of linear evaluation of data.
  • Linearization of measurement operators for improved estimation.

Main Results:

  • Maximum likelihood and least squares optimization lead to systematic underestimation of fidelity.
  • These methods also result in an overestimation of entanglement.
  • Linear evaluation and linearized operators yield unbiased estimates and reliable error bounds.

Conclusions:

  • Common optimization techniques in QST introduce significant biases.
  • Linear methods offer a computationally simple and reliable alternative for QST.
  • Accurate estimation of quantum states and their properties requires careful selection of tomographic tools.