Measuring the Tangle of Three-Qubit States

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.