Self-testing of a single quantum device under computational assumptions

Tony Metger1 and Thomas Vidick2

1Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
2Department of Computing and Mathematical Sciences, California Institute of Technology, CA 91125, United States

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Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system's state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of $\textit{multiple non-communicating}$ parties, which is difficult to enforce in practice, by a $\textit{single computationally bounded}$ party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.

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[3] Thomas Vidick and Tina Zhang, "Classical proofs of quantum knowledge", arXiv:2005.01691.

[4] Alexandru Gheorghiu and Matty J. Hoban, "Estimating the entropy of shallow circuit outputs is hard", arXiv:2002.12814.

[5] Tony Metger, Yfke Dulek, Andrea Coladangelo, and Rotem Arnon-Friedman, "Device-independent quantum key distribution from computational assumptions", arXiv:2010.04175.

[6] Tomoyuki Morimae, "Information-theoretically-sound non-interactive classical verification of quantum computing with trusted center", arXiv:2003.10712.

[7] Tomoyuki Morimae and Yuki Takeuchi, "Trusted center verification model and classical channel remote state preparation", arXiv:2008.05033.

[8] Kishor Bharti, Maharshi Ray, Zhen-Peng Xu, Masahito Hayashi, Leong-Chuan Kwek, and Adán Cabello, "Graph-Theoretic Framework for Self-Testing in Bell Scenarios", arXiv:2104.13035.

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