Robust and Versatile Black-Box Certification of Quantum Devices

Self-testing refers to the fact that, in some quantum devices, both states and measurements can be assessed in a black-box scenario, on the sole basis of the observed statistics, i.e., without reference to any prior device calibration. Only a few examples of self-testing are known, and they just provide nontrivial assessment for devices performing unrealistically close to the ideal case. We overcome these difficulties by approaching self-testing with the semidefinite programing hierarchy for the characterization of quantum correlations. This allows us to improve dramatically the robustness of previous self-testing schemes; e.g., we show that a Clauser-Horne-Shimony-Holt violation larger than 2.57 certifies a singlet fidelity of more than 70%. In addition, the versatility of the tool brings about self-testing of hitherto impossible cases, such as the robust self-testing of nonmaximally entangled two-qutrit states in the Collins-Gisin-Linden-Massar-Popescu scenario.

Figure 1

The swap concept: Characteristics of black boxes are assessed by considering the effect of swap operations between these black boxes and trusted systems (initialized in the state $|0⟩$ here).

Figure 2

Minimal singlet fidelity as a function of CHSH violation. The solid line denotes a lower bound on the fidelity for generic boxes, the dashed one a lower bound for isotropic boxes. Improved bounds are presented in Ref. [27] using optimized swap operators.

Figure 3

Minimum fidelity of the swapped state with the reference state (7) as a function of the three-outcome Bell inequality ${\mathcal{B}}_{\mathrm{CGLMP}}$.

Figure 4

Estimation of Bob’s measurements. The protocol works in two steps: (1) We implement a full swap of Bob’s box and his trusted qubit that we prepare in state $|\phi ⟩$. (2) We implement measurement $B_y$ and study the resulting statistics.