Asymmetric Steerability of Quantum Discordant States in a One-Sided Semi-Device-Independent way

Superlocality and superunsteerability provide operational characterization of quantum correlations in certain local and unsteerable states respectively. Such quantum correlated states have a nonzero quantum discord. Nonzero quantum discord in both the ways is necessary for quantum correlations pointed out by superlocality. On the other hand, in this work, we demonstrate that a nonzero quantum discord in both the ways is not necessary to demonstrate superunsteerability. To this end, we demonstrate superunsteerability for one-way quantum discordant states. This in turn implies the existence of one-way superunsteerability and also the presence of superunsteerability without superlocality. Superunsteerability for nonzero quantum discord states implies steerability in a one-sided semi-device-independent way. Just like one-way steerability occurs for certain Bell-local states in a one-sided device-independent way, our result shows that one-way steerability can also occur for certain nonsuperlocal states but in a one-sided semi-device-independent way.Comment: 8 pages, 1 figure, comments welcom

Self-testing of any pure entangled state with minimal number of measurements and optimal randomness certification in one-sided device-independent scenario

Certification of quantum systems and their properties has become a field of intensive studies. Here, taking advantage of the one-sided device-independent scenario (known also as quantum steering scenario), we propose a self-testing scheme for all bipartite entangled states using a single family of steering inequalities with the minimal number of two measurements per party. Building on this scheme we then show how to certify all rank-one extremal measurements, including non-projective $d^2$-outcome measurements, which in turn can be used for certification of the maximal amount of randomness from every entangled bipartite state of local dimension $d$, that is, $2\log_2d$ bits. Finally, in a particular case of $d=3$, we extend our self-testing results to the fully device-independent setting.Comment: Corrected and improved version. Comments are welcome

Quantum correlations on the no-signaling boundary: self-testing and more

In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in quantum theory lies strictly between the Bell-local set and the no-signaling set, many questions concerning the geometry of the quantum set remain unanswered. Here, we revisit the problem of when the boundary of the quantum set coincides with the no-signaling set in the simplest Bell scenario. In particular, for each Class of these common boundaries containing $k$ zero probabilities, we provide a $(5-k)$-parameter family of quantum strategies realizing these (extremal) correlations. We further prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations, and provide numerical evidence supporting the robustness of these self-testing results. Candidates of one-parameter families of self-testing correlations from some of these Classes are identified. As a byproduct of our investigation, if the qubit strategies leading to an extremal nonlocal correlation are local-unitarily equivalent, a self-testing statement provably follows. Interestingly, all these self-testing correlations found on the no-signaling boundary are provably non-exposed. An analogous characterization for the set $\mathcal{M}$ of quantum correlations arising from finite-dimensional maximally entangled states is also provided. En route to establishing this last result, we show that all correlations of $\mathcal{M}$ in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements. In turn, we obtain the maximal Clauser-Horne-Shimony-Holt Bell inequality violation by any maximally entangled two-qudit state and a no-go theorem regarding the self-testing of such states.Comment: v3: 16+14 pages, 9 figures, 6 tables; v2: 15+12 pages, 9 figures, 5 tables, robust self-testing results and references added; v1: 12+11 pages, 3 figures, 5 table

Scalable noncontextuality inequalities and certification of multiqubit quantum systems

We propose a family of noncontextuality inequalities and show that they can be used for certification of multiqubit quantum systems. Our scheme, unlike those based on non-locality, does not require spatial separation between the subsystems, yet it makes use of certain compatibility relations between measurements. Moreover, it is scalable in the sense that the number of expectation values that are to be measured to observe contextuality scales polynomially with the number of qubits that are being certified. In a particular case we also show our scheme to be robust errors and experimental imperfections. Our results seem promising as far as certification of physical set-ups is concerned in scenarios where spatial separation between the subsystems cannot be guaranteed.Comment: 17 pages, 4 figure

Certification of two-qubit quantum systems with temporal Non-Contextuality inequality

Self-testing of quantum devices based on observed measurement statistics is a method to certify quantum systems using minimal resources. In Ref. [Phys. Rev. \textbf{A} 101, 032106 (2020)], a scheme based on observing measurement statistics that demonstrate Kochen-Specker contextuality has been shown to certify two-qubit entangled states and measurements without the requirement of spatial separation between the subsystems. However, this scheme assumes a set of compatibility conditions on the measurements which are crucial to demonstrating Kochen-Specker contextuality. In this work, we propose a self-testing protocol to certify the above two-qubit states and measurements without the assumption of the compatibility conditions, and at the same time without requiring the spatial separation between the subsystems. Our protocol is based on the observation of sequential correlations leading to the maximal violation of a temporal noncontextuality inequality. Moreover, our protocol is robust to small experimental errors or noise.Comment: 6 + 7 (supplementary pages). Comments are welco

Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements

While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way, the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of 2log23 random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit a device-independent method for certification of the full Weyl–Heisenberg basis in three-dimensional Hilbert spaces together with a one-sided device-independent method for certification of two-qutrit partially entangled states