Abstract
The development and application of the concept of reductions to IID, taking the form of de Finetti theorems, flourished in “standard” quantum information processing in the last decade and more. The tools used, unfortunately, were not applicable when considering device-independent information processing tasks, where the devices being analysed are uncharacterised. The reductions presented in the thesis, namely the de Finetti reduction (Chap. 8) and the entropy accumulation theorem (Chap. 9), are the first to be applicable in the device-independent setting. As such, they have opened the possibility of a significantly simpler analysis of device-independent information processing tasks.
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Notes
- 1.
We list here questions that are not directly related to the showcases considered in the thesis. For concrete open questions regarding parallel repetition (e.g., extensions of the results) and device-independent quantum key distribution (such as possible improvements and experimental implementations) see Sects. 10.4 and 11.4, respectively.
- 2.
In the case of two-party cryptography, the natural choice to make when trying to use the entropy accumulation theorem is one in which the \({\varvec{{O}}}\) systems belong to the honest party and the \({\varvec{{S}}}\) systems to the dishonest party. One can easily come up with boxes that do not fulfil Eq. (9.4) with these choices.
- 3.
In the considered scenarios the two quantities are not dual to one another; see [3] for the details.
References
Fu H, Miller CA (2018) Local randomness: examples and application. Phys Rev A 97(3):032324
Ribeiro J, Kaniewski J, Helsen J, Wehner S et al (2018) Device independence for two-party cryptography and position verification with memoryless devices. Phys Rev A 97(6):062307
Arnon-Friedman R, Bancal J-D (2019) Device-independent certification of one-shot distillable entanglement. New J Phys 21(3):033010
Jain R, Miller CA, Shi Y (2017) Parallel device-independent quantum key distribution. arXiv:1703.05426
Christandl M, König R, Renner R (2009) Postselection technique for quantum channels with applications to quantum cryptography. Phys Rev Lett 102(2):020504
Christandl M, Renner R (2012) Reliable quantum state tomography. Phys Rev Lett 109(12):120403
Schwemmer C, Knips L, Richart D, Weinfurter H, Moroder T, Kleinmann M, Gühne O (2015) Systematic errors in current quantum state tomography tools. Phys Rev Lett 114(8):080403
Lin P-S, Rosset D, Zhang Y, Bancal J-D, Liang Y-C (2018) Device-independent point estimation from finite data and its application to device-independent property estimation. Phys Rev A 97(3):032309
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Arnon-Friedman, R. (2020). Outlook. In: Device-Independent Quantum Information Processing. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-60231-4_12
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DOI: https://doi.org/10.1007/978-3-030-60231-4_12
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