QUANTUM COMMUNICATION ALGORITHMS IN NOISY ENVIRONMENT WITH WEAK MEASUREMENTS

Abstract

The escalating demand for secure and efficient data transmission has propelled advancements in the field of quantum communication. This thesis explores the potential enhancements in secure data transfer amidst quantum noise through the utilization of quantum communication protocols, specifically focusing on quantum teleportation and quantum remote state preparation. Investigating various scenarios involving the deployment of distinct shared entangled channels in the challenging quantum noise environment is crucial for understanding the implications on quantum information loss due to noise-induced fidelity reduction. The thesis initially scrutinizes the teleportation of a single-qubit state across diverse entangled channels, such as the two-qubit Bell channel, the three-qubit GHZ channel, two/three-qubit cluster states, a highly entangled five-qubit state and the six-qubit state. A comprehensive comparison of the quantum cost for each protocol is presented, followed by an analysis of the impact of six noise models—bit-flip noise, phase-flip noise, bit-phase flip noise, amplitude damping, phase damping, and depolarizing noise—on the teleportation protocol. The investigation reveals a notable decrease in fidelity between the initial and teleported states across all entangled channels as the noise parameter increases. In several cases an upward trend in fidelity is observed. Then the thesis delves into the simulation of a quantum teleportation scheme for a single-qubit message using a GHZ-like entangled state. The simulation, conducted on IBM Quantum Experience utilizing the five-qubit real chips "ibmq_athens" and "ibmq_manila" aligns with theoretical results. Additionally, the scheme’s performance is evaluated in the presence of quantum noise, and fidelity variations are analyzed. The quantum teleportation involves transferring an unknown quantum state of a particle to a distant location, however, remote state preparation allows the preparation of a specific known quantum state at a distance without physically transmitting the particle itself. Therefore, a secure deterministic remote state preparation protocol for arbitrary two-qubit entangled states through a seven-qubit entangled channel. The protocol withstands quantum noise, and fidelity variations against the noise parameter are analyzed. A subsequent security analysis, considering both internal and external attacks, attests to the protocol’s robust security under diverse threats. Furthermore, extending the teleportation schemes, an examination of controlled cyclic teleportation protocol is undertaken. This scheme involves three participants, along with a designated controller, engaging in a cyclic teleportation protocol. Amplitude damping noise affects the cyclic teleportation protocol and lowers the fidelity between the initial state and the teleported state. As a potential solution to the amplitude damping noise, weak measurement and the reversal measurement technique are applied to enhance the fidelity of teleportation. The results are significant and shown with the help of a graphical representation. Taking the notion of qubit to higher-dimensional Hilbert space, the concept of “qudit” is discussed in a bidirectional quantum teleportation scheme in d-dimensions with the context of d-dimensional amplitude damping noise. To counteract the adverse effects of amplitude damping noise, weak measurement operators are extended to higher dimensions, effectively mitigating decoherence and augmenting fidelity. The outcome demonstrates a noteworthy increase in fidelity, as visually depicted through a surface plot illustrating the correlation between fidelity and the noise parameter. Hence, the thesis aims to advance the field of quantum communication by contributing secure and efficient data transmission protocols tailored for noisy environments.