Sudden Death of Genuine Tripartite Entanglement

Songbo Xie, Daniel Younis, Joseph H. Eberly

Published 2022-10-04Version 1

Entanglement sudden death (ESD) is a dynamical physical process [Yu and Eberly, Science 323, 598 (2009)]. It occurs when entanglement is able to vanish abruptly, i.e., with a discontinuous slope as a function of time, even though the entangled qubits themselves evolve steadily and analytically. Two-qubit ESD has been well-described and multiply observed, but it remains a mystery. That is, it has not been possible to identify any initial condition under which a state's dynamics can be confidently predicted to evolve to ESD. This challenge has been frustrated by the lack of a quantitative measure of genuine entanglement even for pure-state systems as small as three qubits. Now, with the help of a newly discovered three-qubit measure [Xie and Eberly, Phys. Rev. Lett 127, 040403 (2021)], and by bringing convex-roof construction and Legendre transforms into play, we are able to describe the mixed-state ESD dynamics of a three-qubit system. An unexpected bonus of this advance is the identification of a condition under which ESD can reliably be anticipated.