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Measuring the Tangle of Three-Qubit States.

Adrián Pérez-Salinas1,2, Diego García-Martín1,2,3, Carlos Bravo-Prieto1,2

  • 1Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.

Entropy (Basel, Switzerland)
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Researchers developed a quantum circuit to simplify unknown three-qubit states. This method estimates tangle, a measure of genuine tripartite entanglement, using variational parameter learning and computational basis measurements.

Keywords:
canonical formquantum algorithmtanglethree-qubit state

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Area of Science:

  • Quantum Information Science
  • Quantum Entanglement Studies

Background:

  • Characterizing multipartite entanglement is crucial for quantum information processing.
  • Quantifying genuine tripartite entanglement, like tangle, requires robust measurement techniques.

Purpose of the Study:

  • To present a quantum circuit for transforming unknown three-qubit states into a canonical form.
  • To enable the estimation of tangle from the canonical form.

Main Methods:

  • Utilizing a quantum circuit with three single-qubit parametrized gates.
  • Employing a variational approach to learn optimal gate parameters.
  • Measuring outcome probabilities in the computational basis after state transformation.

Main Results:

  • The circuit successfully transforms unknown three-qubit states to a canonical form.
  • Direct measurement of the canonical form allows for tangle estimation.
  • Simulations under various noise conditions assessed the method's validity.

Conclusions:

  • The proposed variational quantum circuit provides a pathway to quantify genuine tripartite entanglement.
  • The method is robust and applicable even under noisy quantum computing conditions.