Protocols for quantum information processing on graph states

Abstract

Quantum entanglement is a unique phenomenon that occurs in quantum systems and ensures the feasibility of tasks considered impossible in the classical world. Two such important tasks are superdense coding and quantum teleportation. The strength of these protocols rests on the availability of entangled quantum states, such as the bipartite Bell states. When entanglement is shared among many systems, it gives rise to a richer class of multipartite entangled states. One of the popular multipartite quantum states that are successfully prepared by experimentalists are the graph states. Construction of graph states is as follows: Every node has a qubit and the nodes are connected by edges. All the qubits are initially prepared in the so-called $\ket{+}$ state. All the qubits are entangled using controlled-Z (CZ) operations between every pair of qubits that have an edge in the original graph. In our work, we restrict our study to graph states. In this thesis, we discuss our contribution of quantum information processing protocols using graph states that includes: 1) Recovery from a quantum erasure: We consider the problem of a node failure occurring in a network modeled by a graph. By describing the loss of a qubit due to the failure of a node as a quantum erasure, we present a recovery mechanism for distributed quantum information using purification followed by an error correction procedure. 2) Eavesdropping on the graph state: An eavesdropper uses probe qubits and entangles them with the qubits of the graph state via unitary operations. Following the unitary interaction, the eavesdropper performs measurement on the probe qubits. We investigate the behavior of mutual information between the source and the eavesdropper and that between the source and the destination. We define the disturbance caused to the original graph state and study the efficacy of entanglement. We also come up with a scheme to detect the presence of the eavesdropper and recover from the disturbance caused to the graph state using ideas from coding theory. 3) Quantum channels on a graph state: Measurement based quantum computing is an alternative way of quantum information processing that describes the unitary evolution of a quantum state using the cluster state and well-defined measurements. We use the measurement based quantum computing (MBQC) formalism to describe memoryless quantum channels between any two nodes of a network and also come up with the expressions of the capacity of transmission.