Self testing quantum apparatus

Abstract

We study, in the context of quantum information and quantum communication, a configuration of devices that includes (1) a source of some unknown bipartite quantum state that is claimed to be the Bell state $\Phi^+$ and (2) two spatially separated but otherwise unknown measurement apparatus, one on each side, that are each claimed to execute an orthogonal measurement at an angle $\theta \in \{-\pi/8, 0, \pi/8\}$ that is chosen by the user. We show that, if the nine distinct probability distributions that are generated by the self checking configuration, one for each pair of angles, are consistent with the specifications, the source and the two measurement apparatus are guaranteed to be identical to the claimed specifications up to a local change of basis on each side. We discuss the connection with quantum cryptography. testing quantum apparatus (pp273-286) D. Mayers and A. Yao We study, in the context of quantum information and quantum communication, a configuration of devices that includes (1) a source of some unknown bipartite quantum state that is claimed to be the Bell state $\Phi^+$ and (2) two spatially separated but otherwise unknown measurement apparatus, one on each side, that are each claimed to execute an orthogonal measurement at an angle $\theta \in \{-\pi/8, 0, \pi/8\}$ that is chosen by the user. We show that, if the nine distinct probability distributions that are generated by the self checking configuration, one for each pair of angles, are consistent with the specifications, the source and the two measurement apparatus are guaranteed to be identical to the claimed specifications up to a local change of basis on each side. We discuss the connection with quantum cryptography.

Device-independent tests of quantum channels

“…As a comparison we note that while our approach is top-down, i.e. it aims at characterizing the set of correlations compatible with a given hypothesis, in self-testing[6][7][8][9][10][11] the approach is bottom-up, i.e. it aims at characterizing the set of hypotheses compatible with a given correlation.…”

Certifiable quantum dice

“…The idea that the sole violation of a Bell inequality may be useful to cryptographic tasks by itself is not new, and dates back at least to the first proposals for device-independent quantum key distribution[20,21].Phil. Trans.…”

Verification of Quantum Computation:An Overview of Existing Approaches

“…Since self-testing plays such a crucial role in entanglement-based protocols, let us provide a brief description of the concept. The idea of self-testing was introduced by Mayers and Yao in [69], and is concerned with characterising the shared quantum state and observables of n non-communicating players in a non-local game. A nonlocal game is one in which a referee (which we will later identify with the verifier) will ask questions to the n players (which we will identify with the provers) and, based on their responses, decide whether they win the game or not.…”