Regular Article

Distinguishing different classes of entanglement of three-qubit pure states

¹ Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, Odisha, India
² Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India
³ Delhi Technological University, Shahbad Daulatpur, Main Bawana Road, Delhi 110042, India

^a e-mail: chandan@iopb.res.in

Received: 27 April 2018
Received in final form: 13 June 2018
Published online: 13 September 2018

Abstract

Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under stochastic local operation and classical communication (SLOCC) for three-qubit pure states. These operators have very simple structure and can be obtained from the Mermin’s operator with suitable choice of directions. Moreover, these operators may be implemented in an experiment to distinguish the types of entanglement present in a state. We show that the measurement of only one operator is sufficient to distinguish GHZ class from rest of the classes. It is also shown that it is possible to detect and classify other classes by performing a small number of measurements. We also show how to construct such observables in any basis. We also consider a few mixed states to investigate the usefulness of our operators. Furthermore, we consider the teleportation scheme of Lee et al. [Phys. Rev. A 72, 024302 (2005)] and show that the partial tangles and hence teleportation fidelity can be measured. We have also shown that these partial tangles can also be used to classify genuinely entangled state, biseparable state and separable state.