Quantum Fisher Information in Two-Qubit Pure States

Abstract

In terms of quantum Fisher information (QFI), a quantity χ2 was introduced by Pezzé and Smerzi (Phys. Rev. Lett. 102 100401, 2009). They pointed out that the inequality χ2 < 1 was a sufficient condition for multiparticle entanglement. For the two-qubit symmetric states, we found that the inequality χ2 < 1 is a necessary and sufficient condition for entanglement and spin squeezing, and that χ2 is equal to the second kind of spin squeezing parameter ξ22. For the two-qubit asymmetric states, it is only a sufficient condition. In order to make it a necessary and sufficient condition, we extend the concept of the QFI and χ2, and generalize the relations among the entanglement measurement, the spin squeezing parameters and χ2 in symmetric pure states to arbitrary pure states. © 2010 The Author(s).