npj Quantum Information (Oct 2021)

Self-testing quantum systems of arbitrary local dimension with minimal number of measurements

  • Shubhayan Sarkar,
  • Debashis Saha,
  • Jędrzej Kaniewski,
  • Remigiusz Augusiak

Journal volume & issue
Vol. 7, no. 1
pp. 1 – 5


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Abstract Bell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit–qudit entangled states based on violation of a single d-outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, $${{{\mathrm{log}}}\,}_{2}d$$ log 2 d perfect random bits, while it requires only one random bit to encode the measurement choice.