Parallel self-testing of EPR pairs under computational assumptions
Honghao Fu, Daochen Wang, Qi Zhao
备注：
63 pages; v2: expanded the set of measurements that can be tested, added application to device-independent quantum key distribution, and improved overall presentation; v3: further improved overall presentation, in particular, improved the introduction to Section 4
发表信息：
ICALP 2023; Leibniz International Proceedings in Informatics, Volume 261, pp. 64:1-64:19
Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of $N$ EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to $1$ by an honest quantum device using poly$(N)$ resources. Moreover, we show that any quantum device that fails our protocol with probability at most $ε$ must be poly$(N,ε)$-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.
Device-independent self-testing allows a verifier to certify that potentially malicious parties hold on to a specific quantum state, based only on the observed correlations. Parallel self-testing has recently been explored, aiming to self-test many copies (i.e. a tensor product) of the target state concurrently. In this work, we show that $n$ EPR pairs can be self-tested in parallel through $n$ copies of the well known CHSH game. We generalise this result further to a parallel self-test of $n$ tilted EPR pairs with arbitrary angles, and finally we show how our results and calculations can also…
In spite of many attempts, no local realistic model seems to be able to reproduce EPR-Bell type correlations, unless non ideal detection is allowed. The low efficiency of detectors in all experiments with photons makes the use of the fair sampling assumption unavoidable. However, since this very assumption is false in all existing local realistic models based on inefficient detection, we thus question its validity. We show that it is no more reasonable to assume fair sampling than it is impossible to test, and we actually propose an experimental test which would provides clear cut results in c…
The verification of quantum devices is an important aspect of quantum information, especially with the emergence of more advanced experimental implementations of computation and secure communication. Within this, the theory of device-independent robust self-testing via Bell tests has reached a level of maturity now that many quantum states and measurements can be verified without direct access to the quantum systems: interaction with the devices is solely classical. However, the requirements for this robust level of verification are daunting and require high levels of experimental accuracy. In…
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Non-local games and communication complexity with noisy entanglement
Quantum Computing Research Centre（量子计算研究中心）；Hon Hai (Foxconn) Research Institute（鸿海（富士康）研究院）；Institute for Quantum Computing（量子计算研究所）；University of Waterloo（滑铁卢大学）
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