Quantum tomography of three-qubit state

This paper presents a significant advancement in the field of quantum tomography, specifically focusing on the canonical form of three-qubit states, which are increasingly vital in quantum computing and quantum information processing. The motivation for this research arises from the need to accurately characterize pure three-qubit states in the presence of environmental disturbances, particularly amplitude-damping noise. Our analysis reveals that measurement probabilities obtained from generalized single-qubit Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) are sufficient for uniquely determining the quantum state, even in the presence of noise. A key innovation of this study is its thorough exploration of how amplitude-damping noise not only affects the measurement process but also influences the quantum state. We demonstrate that entanglement between qubits plays a crucial role in this context; specifically, we establish that any qubit entangled with a qubit affected by noise is also subjected to its effects. This insight highlights the interconnected nature of qubits in multi-qubit systems and the implications for state reconstruction. The findings of this research contribute a robust framework for state reconstruction in noisy environments, which is essential for the advancement of fault-tolerant quantum computing and secure quantum communication protocols. By elucidating the relationship between measurement probabilities and noise parameters, we enhance the understanding of the resilience of quantum state tomography techniques, thereby improving their applicability in practical quantum technologies. This work not only strengthens the theoretical foundations of quantum information science but also lays the groundwork for implementing these principles in real-world scenarios.