Self-testing refers to a way of uniquely identifying an uncharacterized quantum device based solely on certain extremal quantum correlations. It is known that in the ideal case of a two-qubit singlet all the extremal points that can be obtained by measuring the singlet form the whole criteria for self-testing the singlet and the associated measurements. To make these self-testing criteria more suitable for practical applications, relevant robustness bounds are necessary to discuss. However, the previous robustness analyses for these criteria were obtained by the swap method, which may not be guaranteed to be tight. In this paper, we construct a general extraction map applying to all self-testing criteria of the singlet state with two binary measurements for each party and derive analytic robustness bounds for a self-testing singlet in different regions of the boundary of the extremal quantum correlation set. The comparison shows that our robustness bounds are better than the known results and close to optimal for these self-testing criteria of a singlet state with two binary measurements.
Self-testing refers to a way of uniquely identifying an uncharacterized quantum device based solely on certain extremal quantum correlations. It is known that in the ideal case of a two-qubit singlet all the extremal points that can be obtained by measuring the singlet form the whole criteria for self-testing the singlet and the associated measurements. To make these self-testing criteria more suitable for practical applications, relevant robustness bounds are necessary to discuss. However, the previous robustness analyses for these criteria were obtained by the swap method, which may not be guaranteed to be tight. In this paper, we construct a general extraction map applying to all self-testing criteria of the singlet state with two binary measurements for each party and derive analytic robustness bounds for a self-testing singlet in different regions of the boundary of the extremal quantum correlation set. The comparison shows that our robustness bounds are better than the known results and close to optimal for these self-testing criteria of a singlet state with two binary measurements.
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.
Self-testing refers to the phenomenon that certain extremal quantum correlations (almost) uniquely identify the quantum system under consideration. For instance, observing the maximal violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality certifies that the two parties share a singlet. While self-testing results are known for several classes of states, in many cases they are only applicable if the observed statistics are almost perfect, which makes them unsuitable for practical applications. Practically relevant self-testing bounds are much less common and moreover they all result from a single numerical method (with one exception which we discuss in detail). In this work we present a new technique for proving analytic self-testing bounds of practically relevant robustness. We obtain improved bounds for the case of self-testing the singlet using the CHSH inequality (in particular we show that nontrivial fidelity with the singlet can be achieved as long as the violation exceeds β^{*}=(16+14sqrt[2])/17≈2.11). In the case of self-testing the tripartite Greenberger-Horne-Zeilinger state using the Mermin inequality, we derive a bound which not only improves on previously known results but turns out to be tight. We discuss other scenarios to which our technique can be immediately applied.
Self-testing is a method with which a classical user can certify the state and measurements of quantum systems in a device-independent way. In particular, self-testing of entangled states is of great importance in quantum information processing. An understandable example is that the maximal violation of the Clauser-Horne-Shimony-Holt inequality necessarily implies that the bipartite system shares a singlet. One essential question in self-testing is that, when one observes a nonmaximum violation, how far is the tested state from the target state (which maximally violates a certain Bell inequality)? The answer to this question describes the robustness of the used self-testing criterion, which is highly important in a practical sense. Recently, J. Kaniewski derived two analytic self-testing bounds for bipartite and tripartite systems. In this Letter, we experimentally investigate these two bounds with high-quality two-qubit and three-qubit entanglement sources. The results show that these bounds are valid for various entangled states that we prepared. Thereby, a proof-of-concept demonstration of robust self-testing is achieved, which improves on the previous results significantly.
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 show that exact self-testing of a quantum correlation does not imply robust self-testing. Mančinska and Schmidt previously established such a separation for non-local games, but their obstruction to robustness arises from two distinct optimal correlations, with the self-tested one remaining robust. We establish the separation for a single correlation.
Our proof is operator-algebraic. The main technical contribution is a general construction that associates a synchronous binary correlation to any finitely presented C*-algebra with unitary generators and real-coefficient relations. The implementing states of the correlation correspond exactly to the tracial states on the algebra. We apply this construction to an algebra with a unique finite-dimensional tracial state and a distinct amenable tracial state. By a characterization established by Zhao and independently by Kar, the resulting correlation is a self-test but not a robust self-test.
Self-testing is the high-level security verification of a claimed quantum device, confirming the quantum states prepared in the device and the measurements performed based solely on the observed statistics. The statistical correlations can realize the self-testing of the quantum system in the preparing-and-measuring scenario. However, most of previous studies focused on the self-testing of shared entangled states between devices, at present only a few researches are presented and the existing work can only simultaneously self-test the states and measurements when some witness inequalities reach a maximum violation. We focus on four-state preparation and the selected scenarios of two measurements. In this scenario, Armin Tavakoli et al. [Tavakoli A, Kaniewski J, Vértesi T, Rosset D, Brunner N 2018 Phys. Rev. A 98 062307] have put forward a criterion based on the dimensional witness violation inequality which can achieve BB84 particles and corresponding Pauli measurements. However, in addition to the maximum violation of the inequality, any statistics with deviation from the maximum deviation cannot be self-tested. Besides, only the BB84 particle preparation and measurements system can be self-tested with that criterion, resulting in a large number of four-state preparation and two measurement systems that cannot be self-tested. Therefore, in this work, in addition to the maximum violation of that dimension inequality, we directly focus on the full observed statistics and further propose some new criteria for self-testing qubit quantum systems in the preparing-and-measiuring scenarios. And the self-testing criteria are proven in an ideal case. We construct a local isometry by using the constructions commonly used in device-independent cases, exchange the target system with the additional system, and realize the self-testing of more qubit state sets and measurement sets than BB84 particles. This meets the requirements for practical experiments to realize various tasks by different quantum state sets. In addition, we perform a robust analysis of the proposed criteria and use fidelity to describe the closeness of the state to the ideal state of the auxiliary system. Finally, an improved dimensional-dependent NPA method is used to optimize the lower bound of the robustness, making the new criteria practical under experimental noise. We use the YALIMP software package in MATLAB and the solver SEDUMI to solve this optimization problem. The present research increases the diversity of qubit state preparations and self-testing of measurement system, which is beneficial to the actual self-testing of different non-entangled single quantum systems.