Using linear and nonlinear entanglement witnesses to generate and detect
  bound entangled states on an IBM quantum processor
We investigate bound entanglement in three-qubit mixed states which are
diagonal in the Greenberger-Horne-Zeilinger (GHZ) basis. Entanglement in these
states is detected using entanglement witnesses and the analysis focuses on
states exhibiting positive partial transpose (PPT). We then compare the
detection capabilities of optimal linear and nonlinear entanglement witnesses.
In theory, both linear and nonlinear witnesses produce non-negative values for
separable states and negative values for some entangled GHZ diagonal states
with PPT, indicating the presence of entanglement. Our experimental results
reveal that in cases where linear entanglement witnesses fail to detect
entanglement, nonlinear witnesses are consistently able to identify its
presence. Optimal linear and nonlinear witnesses were generated on an IBM
quantum computer and their performance was evaluated using two bound entangled
states (Kay and Kye states) from the literature, and randomly generated
entangled states in the GHZ diagonal form. Additionally, we propose a general
quantum circuit for generating a three-qubit GHZ diagonal mixed state using a
six-qubit pure state on the IBM quantum processor. We experimentally
implemented the circuit to obtain expectation values for three-qubit mixed
states and compute the corresponding entanglement witnesses.
Vaishali Gulati Gayatri Singh Kavita Dorai