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Information geometry of controlled quantum open systems


Project Description

This project will be based at the University of Nottingham in the School of
Mathematical Sciences and the School of Physics and Astronomy. The PhD candidate will take part in the activities of the newly established “Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems”.

We are currently witnessing the dawn of a new technology revolution based on the exploitation of quantum effects, with applications in metrology, computation, information transmission, and quantum simulations [1]. As real quantum systems are affected by noise and decoherence, the study of open quantum systems and their control is fundamental for successfully implementing such technologies [2]. This PhD project aims to further expand our understanding of open dynamics by exploiting new insights from complementary areas such as non-equilibrium statistical mechanics, quantum control, quantum information and quantum metrology.

Our research has shown that open systems exhibiting “dynamical phase transitions” generate output fields that could be used as high precision probes in quantum metrology [3]. The next step will be to investigate efficient measurement strategies, for instance by means of quantum “post-processing” using tools from quantum networks theory [4], and explore the use of alternative input states and feedback control for achieving enhanced precision. Another direction is towards a better understanding of the “information geometry” of open systems [5] and the connection with related concepts developed in non-equilibrium statistical mechanics and quantum information. Further research topics include the fluctuation theory for output fields, dimensional reduction methods, filter stability and state purification for continuous-time measurements.

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit the University Of Nottingham application page:
http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx

For any enquiries please email:

Funding Notes

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics or Physics preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

References

[1] M. A. Nielsen I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, (2000)

[2] H. Wiseman, G. Milburn, Quantum Measurement and Control, Cambridge University Press, (2014)

[3] K. Macieszczak, M. Guta, I. Lesanovsky, J. P. Garrahan
Dynamical phase transitions as a resource for quantum enhanced metrology
Phys. Rev. A 93, 022103 (2016)

[4] J. Gough and M. R. James, The Series Product and Its Application to Quantum Feedforward and Feedback Networks
IEEE Trans. Automatic Control 54 2530 (2009)

[5] M. Guta, J. Kiukas, Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics, ArXiv:1601.04355

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