In this dissertation two quantum information processes are studied, entanglement swapping and quantum dense coding. Entanglement swapping is used as a fundamental building block in quantum relays and quantum repeaters for long distance communication. Quantum dense coding is a process of communication by sending two bits of classical information using only one qubit. These processes are described here in realistic scenarios by taking into account imperfect sources of entangled photon pairs and detectors. Moreover, detectors used in quantum optical experiments occasionally produce dark counts and do not always detect incoming photons. These imperfections need to be taken into account when performing calculations involving detectors as in the cases of entanglement swapping and dense coding.

The conditional probabilities of different imperfect detectors and the state generated by two parametric down-conversion (PDC) sources after entanglement swapping are also discussed here. The four fold coincidence probability for entanglement swapping process including all imperfections is discussed in this dissertation. Furthermore, we modeled realistically the experimental dense coding process up to some extent. In this case we calculated the quantum state produced by a single realistic PDC source. We also calculated the probability to detect this state at the detectors in the case of ideal detection. The effect of non linearity of PDC crystal on this probability is also discussed here.

Student Name

Sadia Hassan

Project Title

Error Correction in Quantum Cryptography.

Desciption

Quantum information theory is a new field that attempts to quantify and describe quantum mechanical resources and the processes that act on them. It provides a foundation for such topics as quantum cryptography, quantum error-correction and quantum teleportation. Quantum cryptography provides secure communication between legitimate users even in the presence of an adversary by making possible the distribution of a secret key. It then allows error correction and privacy amplification, which is elimination of adversary information, through classical communication. The objective of this thesis is to present the working principle of quantum cryptography and to give examples of quantum cryptography protocols and their implementations using two way classical communications. An elementary derivation of best symmetric eavesdropping strategies for the four-state BB84 quantum cryptography protocol for incoherent attacks is reviewed. The entanglement-purification protocol by Gottesman and Lo’s standard quantum key distribution scheme’s vis BB84 and the six-state scheme, are studied in detail with two-way communications against the most general attack. This protocol is based on two-way entanglement purification which can tolerate a bit error rate up to 20% for BB84 and 26.4% for six-state scheme respectively. Further we have modified this scheme for higher number of qubits by using the three-qubit gate i.e. Toffoli gate. This modified key distribution protocol is unconditionally secure and has a tolerable error rate of 20%.

Student Name

Sidra Shafiq

Project Title

Application of Dirac equation with Coulomb-like QCD potential for understanding light and heavy meson states mass spectroscopy

Desciption

Dirac equation has been reviewed with particular reference to its exact solution for Hydrogen atom, which explains the spin-orbit splitting for Hydrogen-like atoms. Hadron spectroscopy has been reviewed, in particular the hyperne and spin-orbit splitting in the meson spectroscopy is discussed. The hyperne splitting can be satisfactorily explained by Fermi spin-spin interaction within the framework of One Gluon exchange (OGE) potential in QCD. The spin-orbit splitting is experimentally suppressed. This suppression can be understood within the framework of Dirac theory where Dirac hamiltonian shows a dynamical spin symmetry provided that Vv(r) = Vs(r) + U ,where Vv(r) is the 4th component of the vector potential and Vs(r) is the Lorentz scalar. In this case the spin-orbit splitting vanishes. This symmetry is re-derived when the Dirac equation is written in the two-component pauli-form in a transparent way. Furthermore it is shown that Dirac equation can be solved exactly if both Vv(r) and Vs(r) are Coulomb like. Within this framework the spin-orbit splitting is calculated for qQ and Qq meson states, where q is light quark and Q is heavy quark.