Self-testing through EPR-steering

Abstract

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 this paper we discuss the possibility of self-testing where we have direct access to part of the quantum device. This motivates the study of self-testing via EPR-steering, an intermediate form of entanglement verification between full state tomography and a Bell test. Quantum non-locality implies EPR-steering so results in the former can apply in the latter, but we ask what advantages may be gleaned from the latter over the former given that one can do partial state tomography. We show in the case of self-testing a maximally entangled two-qubit state, or ebit, EPR-steering allows for simpler analysis and better error tolerance than in the case of full device-independence. On the other hand, this improvement is only a constant improvement and (up to constants) is the best one can hope for. Finally, we indicate that the main advantage in self-testing based on EPR-steering could be in the case of self-testing multi-partite quantum states and measurements. For example, it may be easier to establish a tensor product structure for a particular party's Hilbert space even if we do not have access to their part of the global quantum system.

18+3 pages, 5 figures. New published version with some alterations in response to referees and typos corrected. We acknowledge discussions with Alexandru Gheorghiu, Petros Wallden and Elham Kashefi about their independent work that recently appeared as arXiv:1512.07401. Comments welcome

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• Experimentally Certified Transmission of a Quantum Message through an Untrusted and Lossy Quantum Channel via Bell's Theorem
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• Simultaneous Certification of Entangled States and Measurements in Bounded Dimensional Semi-Quantum Games
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