Experimentally feasible semi-device-independent certification of four-outcome positive-operator-valued measurements

Recently the quantum information science community devoted a lot of attention to the theoretical and practical aspects of generalized measurements, the formalism of all possible quantum operations leading to acquisition of classical information. On the other hand, due to imperfections present in quantum devices, and limited thrust to them, a trend of formulating quantum information tasks in a semi-device-independent manner emerged. In this Rapid Communication we use the concept of quantum random access codes to construct a protocol able to certify the presence of the generalized measurements in a semi-device-independent way without employing quantum entanglement. We use semidefinite programming methods to show robustness of the protocol and characterize its statistical properties. We conclude that it allows for experimental realizations using technology currently available in laboratories.

Figure 1

The values of upper bounds $g_3\left(k\right)$ and $g_2\left(k\right)$ for the game (7) possible to be obtained with three- and two-outcome POVMs, respectively, for different values of $k$.