Abstract This chapter is devoted to deviice-independent self-testing. This refers to the fact that some extremal behaviors in the quantum set can actually be realised only with specific measurements on a specific shared entangled state. The two main examples, namely the maximal value of CHSH and the Mayers-Yao test, are described in detail before the abstract definition of self-testing is given.
Abstract This chapter is devoted to deviice-independent self-testing. This refers to the fact that some extremal behaviors in the quantum set can actually be realised only with specific measurements on a specific shared entangled state. The two main examples, namely the maximal value of CHSH and the Mayers-Yao test, are described in detail before the abstract definition of self-testing is given.
Self-testing refers to the possibility of characterizing uniquely (up to local isometries) the state and measurements contained in quantum devices, based only on the observed input-output statistics. Already in the basic case of the two-qubit singlet, self-testing is not unique: the two known criteria (the maximal violation of the CHSH inequality and the Mayers–Yao correlations) are not equivalent. It is unknown how many criteria there are. In this paper, we find the whole set of criteria for the ideal self-testing of a singlet with two measurements and two outcomes on each side; it coincides with all the extremal points of the quantum set that can be obtained by measuring the singlet.
Abstract Self-testing, which refers to device independent characterization of the state and the measurement, has been intensively studied in quantum information theory. One of the implicit assumptions in self-testing theorem is, measurement settings should be chosen randomly and independently by each party. The relaxation of this assumption potentially gives untrusted device providers the power to control the device with no quantum feature, even fake the quantum behavior by using the classical strategies within the device. In this paper, we analyze the effects of the reduced measurements independence on self-testing two-qubit entangled states based on the violation of Bell inequalities. By assuming adversary’s capabilities, we show to achieve the maximum CHSH violation in this case, four different state-measurements preparations should be provided. Without run information one could not really self-test the underlying system in each run anymore, but it must be equal with one of four entangled systems up to local unitaries.
Device-independent certification, also known as self-testing, aims at guaranteeing the proper functioning of untrusted and uncharacterized devices. For example, the quality of an unknown source expected to produce two-qubit maximally entangled states can be evaluated in a bipartite scenario, each party using two binary measurements. The most robust approach consists in deducing the fidelity of produced states with respect to a two-qubit maximally entangled state from the violation of the CHSH inequality. In this paper, we show how the self-testing of two-qubit maximally entangled states is improved by a refined analysis of measurement statistics. The use of suitably chosen Bell tests, depending on the observed correlations, allows one to conclude higher fidelities than ones previously known. In particular, nontrivial self-testing statements can be obtained from correlations that cannot be exploited by a CHSH-based self-testing strategy. Our results not only provide insight into the set of quantum correlations suited for self-testing, but also facilitate the experimental implementations of device-independent certifications.
Abstract Quantum nonlocality has recently been intensively studied in connection to device-independent quantum information processing, where the extremal points of the set of quantum correlations play a crucial role through self-testing. In most protocols, the proofs for self-testing rely on the maximal violation of the Bell inequalities, but there is another known proof based on the geometry of state vectors to self-test a maximally entangled state. We present a geometrical proof in the case of partially entangled states. We show that, when a set of correlators in the simplest Bell scenario satisfies a condition, the geometry of the state vectors is uniquely determined. The realization becomes self-testable when another unitary observable exists on the geometry. Applying this proven fact, we propose self-testing protocols by intentionally adding one more measurement. This geometrical scheme for self-testing is superior in that, by using this as a building block and repeatedly adding measurements, a realization with an arbitrary number of measurements can be self-tested. Besides the application, we also attempt to describe nonlocal correlations by guessing probabilities of distant measurement outcomes. In this description, the quantum set is also convex, and a large class of extremal points is identified by the uniqueness of the geometry.
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.
We consider the problem of one-sided device-independent self-testing of any pure entangled two-qubit state based on steering inequalities which certify the presence of quantum steering. In particular, we note that in the 2-2-2 steering scenario (involving two parties, two measurement settings per party, and two outcomes per measurement setting), the maximal violation of a fine-grained steering inequality can be used to witness certain extremal steerable correlations, which certify all pure two-qubit entangled states. We demonstrate that the violation of the analogous Clauser-Horne-Shimony-Holt inequality of steering or the nonvanishing value of a quantity constructed using a correlation function called mutual predictability, together with the maximal violation of the fine-grained steering inequality, can be used to self-test any pure entangled two-qubit state in a one-sided device-independent way.