From interaction-free measurement to weak values - applications and issues from quantum foundations for quantum technologies

This PhD project involves investigating foundational areas in quantum physics (such as interaction-free measurement, weak values, and statistical independence violation), with a view to evaluating and leveraging the effects these novel phenomena/areas have for the development of quantum technologies. Thus it falls within EPSRC research themes in Quantum Technologies and Physics research area Quantum Optics and Information. The project initially focussed on counterfactual/interaction-free effects -both looking at philosophical/foundational issues [1,2], and potential practical applications [3,4,5]. While this research is still ongoing the scope has expanded onto the question of how we define the presence/path of a quantum particle. This covers philosophical aspects and interactions with an environment which could cause information leakage/decoherence. This naturally led into looking at weak values/measurement of path projection operators [6,7], as well as to what extent the wavefunction just represents our (incomplete) knowledge of a system, rather than really representing the way the world is [8,9]. From this, we have developed an external collaboration with Prof Tim Palmer FRS and Dr Sabine Hossenfelder, looking at extensions of quantum mechanics which allow us to regain Bell-locality by weakening statistical independence [10-13]. These interpretations - which could act as a path to unifying quantum mechanics with general relativity - also lead to different predictions to standard quantum mechanics on scales we are only now beginning to probe (e.g. using noisy intermediate-scale quantum devices), and could very much affect claims being made by the quantum community. The project contributes to the underpinning science of quantum technologies, adapting quantum foundational ideas into quantum technological applications (e.g. [3,4,5]), and evaluating current quantum technologies (e.g. quantum key distribution, quantum computing) in light of potential extensions of quantum mechanics.
Current aims for the last year-and-a-half of the project are:
- Developing a protocol for counterfactual polarimetry
- Investigating how the violation of statistical independence allows us to treat the von Neumann equation as a Liouville equation (avoiding negative quasi-probabilities)
- Investigating the effects of statistical independence violation in more depth on current/developing quantum technologies.
[1] Salih, H., McCutcheon, W., Hance, J., & Rarity, J. (2018). arXiv:1806.01257.
[2] Hance, J. R., Ladyman, J., & Rarity, J. (2021). Found Physics, 51, 1.
[3] Salih, H., Hance, J. R., McCutcheon, W., Rudolph, T., & Rarity, J. (2021). New Journal of Physics, 23(1), 013004.
[4] Salih, H., Hance, J. R., McCutcheon, W., Rudolph, T., & Rarity, J. (2020). arXiv:2009.05564.
[5] Hance, J. R., & Rarity, J. (2021). Counterfactual ghost imaging. npj Quantum Information, 7(1), 1-7.
[6] Hance, J., & Rarity, J. (2021). Optik, 167451.
[7] Hance, J. R., Rarity, J., & Ladyman, J. (2021). arXiv:2109.14060.
[8] Hance, J. R., Rarity, J., & Ladyman, J. (2021). arXiv:2101.06436.
[9] Hance, J. R., & Hossenfelder, S. (2021). arXiv:2109.02676.
[10] Hance, J. R., Hossenfelder, S., & Palmer, T. N. (2021). arXiv:2108.07292.
[11] Hance, J. R., Hossenfelder, S., & Palmer, T. N. (2021). arXiv:2108.08144.
[12] Hance, J. R., Palmer, T. N., & Rarity, J. (2021) arXiv:2102.07795.
[13] Bracken, C., Hance, J.R., & Hossenfelder, S. (2021) arXiv:2111.09347.