Quantum information and quantum foundations
The development of quantum technologies presents both a chance to exploit to exotic quantum phenomena and also new questions for the foundations of quantum theory. We have a continuing interest and expertise in the forms of optimal measurements, including discrimination between a number of possible quantum states [1-3]. Such ideas are important, in particular, in quantum communications and we have an active interest in the study of quantum cryptography [4-5].
Pushing the limits of what is possible has encouraged investigation of rival formulations including the so-called PT-symmetric extension and also time-reversed or retrodictive quantum theory. We have shown that the former, when correctly formulated is fully compatible with conventional quantum theory and, contrary to some claims does not allow for violation of well-established bounds [6]. The retrodictive form embodies a synthesis of conventional predictive quantum theory with Bayes’ theorem and we have used this as the basis of a practical approach to image reconstruction [7,8].
References
[1] Difficulty of distinguishing product states, Sarah Croke and Stephen M. Barnett; Physical Review A 95, 012337 (2017).
[2] Optimal sequential measurements for bipartite state discrimination, Sarah Croke, Stephen M. Barnett and Graeme Weir; Physical Review A 95, 052308 (2017).
[3] Optimal discrimination of single-qubit mixed states, Graeme Weir, Stephen M. Barnett and Sarah Croke; Physical Review A 96, 022312 (2017).
[4] Cavity-enabled high-dimensional quantum key distribution, Thomas Brougham and Stephen M. Barnett; Journal of Physics B: Atomic, Molecular and Optical Physics 47, 155501 (2014).
[5] The information of high-dimensional time-bin encoded photons, Thomas Brougham, Christoph F. Wildfeuer, Stephen M. Barnett and Daniel J. Gauthier; European Physical Journal D 70, 214 (2016).
[6] PT-symmetric Hamiltonians and their application in quantum information, Sarah Croke, Phys. Rev. A 91, 052113 (2015)
[7] Image retrodiction at low light levels, Matthias Sonnleitner, John Jeffers and Stephen M. Barnett; Optica 2, 950 (2015).
[8] From retrodiction to Bayesian quantum imaging, Fiona C. Speirits, Matthias Sonnleitner and Stephen M. Barnett; Journal of Optics 19, 04401 (2017).