Generalized Quantum Tomography Algorithm Achieves Efficient State Estimation through Collective Measurements

Quantum tomography, a vital technique for characterizing and verifying quantum systems, underpins advances in quantum technologies and fundamental physics. Shuixin Xiao Petersen and Yuanlong Wang, alongside Zhibo Hou, Aritra Das, and Farhad Farokhi, have significantly extended this field with a new framework for generalized collective quantum tomography. Their work moves beyond estimating single unknown states, instead tackling the more complex challenge of characterizing collections of identical or distinct quantum states, detectors, or processes simultaneously. The team develops three novel algorithms, each designed for a specific tomography task, and rigorously analyses their computational complexity and accuracy, demonstrating substantial improvements over existing methods and approaching fundamental limits on measurement precision, particularly by effectively utilising information about state purity.

Opening our understanding of quantum mechanics, collective quantum state tomography estimates an unknown quantum state through joint measurements on multiple copies of that state, offering superior information extraction efficiency. This work extends this framework to a generalized setting where the target can be a quantum state, a detector, or a quantum process, each potentially identical or distinct. The researchers formulate these tasks as optimization problems and develop algorithms for collective quantum state, detector, and process tomography, accompanied by detailed analysis of computational complexity.

Australian and Chinese Quantum Research Collaboration

This international collaboration brings together leading quantum scientists from Australia and China, focusing on the development of advanced techniques for quantum control and information processing. Their combined expertise spans quantum system identification, control theory, quantum metrology, and machine learning.

Collective Tomography via Tensor Optimization

Scientists have developed a generalized framework for collective quantum state tomography, detector tomography, and process tomography, formulating each task as a tensor-structured optimization problem. This work extends existing techniques to simultaneously characterize quantum states, measurement devices, and quantum processes, achieving improved accuracy and efficiency. The team’s algorithms consistently outperform existing methods, reducing measurement errors and approaching theoretical limits of precision. Experiments utilizing two-copy collective measurements directly provide information about the purity of the quantum state, a property inaccessible through individual measurements, and the algorithms effectively leverage this purity information. Validation using experimental data from photonic quantum walks demonstrated the effectiveness of the algorithms, delivering a powerful new toolkit for characterizing quantum systems and advancing quantum technologies.

Collective Quantum Tomography of States and Processes

This work extends the framework of collective quantum state tomography to encompass not only states, but also detectors and processes, representing a significant advance in quantum characterization techniques. Researchers developed algorithms to estimate these quantum objects through joint measurements on multiple copies, formulating the tasks as optimization problems and rigorously characterizing their computational complexity and accuracy. The team demonstrated that their methods, employing both closed-form solutions and sum of squares optimization, achieve lower mean squared errors compared to existing algorithms, approaching the fundamental collective measurement bound. Experimental validation, utilizing two-copy collective measurements, confirmed the effectiveness of the approach, particularly in leveraging information about state purity.

The algorithms were successfully applied to pure quantum states, projective measurements, and unitary processes, demonstrating broad applicability. While the sum of squares optimization approach offers higher accuracy, it comes at the cost of increased computational demands, and future research will focus on developing adaptive algorithms and extending the techniques to larger, more complex quantum systems. This work represents a substantial step towards more efficient and accurate quantum characterization, with implications for advancing quantum technologies and fundamental understanding of quantum mechanics.