Investigations on Discrete Wigner Functions of multi-qubit quantum systems
ABSTRACT :
Discrete Wigner Functions (DWFs) are the generalization of Wigner functions to the finite dimensional quantum systems. These functions are extensively used in the field of quantum information and quantum computation, especially in quantum error correction, quantum teleportation and in quantum computational speed-up. Though several non-unique versions of DWFs are available in the literature, the construction given by Wootters and Gibbons et al., is particularly elegant and it is developed based on the finite fields and mutually unbiased basis. In this talk, I will introduce the Wootters and construction of DWFs and discuss our recent results in this field. I will present the method of performing spin flip operation in discrete phase space which is central for quantifying entanglement present in the multi-qubit systems. The discussion covers the relationship between DWF and Stokes vector and the generalized reduction formula for DWFs of multi-qubit systems. I will also present our experimental procedure to generate two qubit polarization entangled photons and the method of reconstructing the DWFs of these two photon polarization states.