Experimental demonstration of one-sided device-independent self-testing of any pure two-qubit entangled state

Abstract

We demonstrate one-sided device-independent self-testing of any pure entangled two-qubit state based on a fine-grained steering inequality. The maximum violation of a fine-grained steering inequality can be used to witness certain steerable correlations, which certify all pure two-qubit entangled states. Our experimental results identify which particular pure two-qubit entangled state has been self-tested and which measurement operators are used on the untrusted side. Furthermore, we analytically derive the robustness bound of our protocol, enabling our subsequent experimental verification of robustness through state tomography. Finally, we ensure that the requisite no-signalling constraints are maintained in the experiment.

Experimental Demonstration of Fine-Grained Steering Inequality of Two-Qubit Mixed States

“…The experimental demonstration of the FGS inequality of any two-qubit pure entangled states has been realized in Ref. [18]. In this article, we provide experimental evidence of FGS inequality in mixed states via linear optical elements.…”

“…For simplicity, we specify that Bob's observable is taken from the set {σ z , σ x }, therefore, the left-hand side of Equation ( 5) hits the maximum value when Alice applies the same set of observables on her system. The reason is that the Equation ( 6) states are constructed by introducing completely decoherence in maximally entangled pure state |ψ + , which violates Equation ( 5) maximally when Alice and Bob apply the same observables {σ z , σ x } simultaneously [18]. In this case, the left-hand side of Equation ( 5) obviously becomes:…”

“…Note that Bell diagonal states are a linear superposition of the maximally entangled states |ψ ± , according to Ref. [18], for |ψ ± , the maximum value of the left-hand side of Equation ( 5), P(0 B 1 |0 A 1 ) + P(0 B 2 |0 A 2 ) = 2 is achieved for Alice's choices {σ z , ±σ x } when fixing Bob's measurement observables as {σ z , σ x }. Thus, we can easily calculate that when p < 0.5, Alice should apply the measurement {σ z , −σ x } on her subsystem, the corresponding is {σ z , σ x } on her side if p ≥ 0.5.…”

“…Thus, quantum steering is usually connected with the secret key rate in one-sided device-independent quantum key distribution [14,15]. Apart from this, quantum steering shows the advantages to self-test pure entangled states [16,17] and discriminate quantum states [18].…”

Robust certification of arbitrary outcome quantum measurements from temporal correlations

“…Semi device-independent self-testing protocols have also been investigated [20][21][22][23][24] employing Einstein-Podolsky-Rosen steering.…”