Southwest Quantum Information and Technology

Triangle measure of tripartite entanglement

Presenting Author: Songbo Xie, University of Rochester
Contributing Author(s): Joseph H. Eberly

Although multi-party entanglement has been demonstrated for a large number of qubits, finding a genuine entanglement measure even for three-qubits has been found difficult, despite the fact that two-qubit entanglement measures have been studied well. One two-qubit entanglement measure is concurrence, satisfying 1 ≥ C ≥ 0. The value 0 implies no entanglement, while the value 1 refers the maximal entanglement of the qubits, in a Bell state. However, a three-qubit entanglement measure has to satisfy the following two conditions to be called a genuine multipartite entanglement (GME) measure: (a) GME=0 for biseparable and product states. (b) GME>0 for nonbiseparable states. Most existing tripartite measures cannot meet the above conditions. We will present the first clear example of a three-qubit GME measure that properly assigns relative state indformation. The concurrence relation developed by Qian, Alonso, and Eberly for an arbitrary three-qubit pure system implies a geometric triangle, with lengths of its edges given by the three one-to-other concurrences in squared form. We call this a concurrence triangle. Concurrence triangle AREA was found by us to satisfy both conditions (a) and (b), and is also a proper GME measure named concurrence FILL. Specific examples will be illustrated to show that different tripartite GME measures are inequivalent and that the triangle-based concurrence Fill is superior to the other GMEs by containing more information about the systems.

Read this article online: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.040403?ft=1

(Session 5 : Thursday from 12:00pm-2:00 pm)