Recently, Tavakoli et al. proposed a self-testing scheme in the prepare-and-measure scenario, showing that self-testing is not necessarily based on entanglement and violation of a Bell inequality [Phys. Rev. A 98 062307 (2018)]. They realized the self-testing of preparations and measurements in an <?CDATA $N\to 1$?> N → 1 ( <?CDATA $N\ge 2$?> N ≥ 2 ) random access code (RAC), and provided robustness bounds in a <?CDATA $2\to 1$?> 2 → 1 RAC. Since all <?CDATA $N\to 1$?> N → 1 RACs with shared randomness are combinations of <?CDATA $2\to 1$?> 2 → 1 and <?CDATA $3\to 1$?> 3 → 1 RACs, the <?CDATA $3\to 1$?> 3 → 1 RAC is just as important as the <?CDATA $2\to 1$?> 2 → 1 RAC. In this paper, we find a set of preparations and measurements in the <?CDATA $3\to 1$?> 3 → 1 RAC, and use them to complete the robustness self-testing analysis in the prepare-and-measure scenario. The method is robust to small but inevitable experimental errors.
Recently, Tavakoli et al. proposed a self-testing scheme in the prepare-and-measure scenario, showing that self-testing is not necessarily based on entanglement and violation of a Bell inequality [Phys. Rev. A 98 062307 (2018)]. They realized the self-testing of preparations and measurements in an <?CDATA $N\to 1$?> N → 1 ( <?CDATA $N\ge 2$?> N ≥ 2 ) random access code (RAC), and provided robustness bounds in a <?CDATA $2\to 1$?> 2 → 1 RAC. Since all <?CDATA $N\to 1$?> N → 1 RACs with shared randomness are combinations of <?CDATA $2\to 1$?> 2 → 1 and <?CDATA $3\to 1$?> 3 → 1 RACs, the <?CDATA $3\to 1$?> 3 → 1 RAC is just as important as the <?CDATA $2\to 1$?> 2 → 1 RAC. In this paper, we find a set of preparations and measurements in the <?CDATA $3\to 1$?> 3 → 1 RAC, and use them to complete the robustness self-testing analysis in the prepare-and-measure scenario. The method is robust to small but inevitable experimental errors.
The goal of self-testing is to characterize an a priori unknown quantum system based solely on measurement statistics, i.e., using an uncharacterized measurement device. Here we develop self-testing methods for quantum prepare-and-measure experiments, thus not necessarily relying on entanglement and/or violation of a Bell inequality. We present noise-robust techniques for self-testing sets of quantum states and measurements, assuming an upper bound on the Hilbert space dimension. We discuss in detail the case of a $2\ensuremath{\rightarrow}1$ random access code with qubits, for which we provide analytically optimal self-tests. The simplicity and noise robustness of our methods should make them directly applicable to experiments.
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.
Violation of the N-partite inequality introduced in Phys. Rev. Lett. 129, 150401 (2022) for genuine multipartite nonlocality under local operations and shared randomness (LOSR) rules out all causal-network models obtained by locally composing arbitrary resources involving at most N−1 parties, even when supplemented by shared randomness among all N parties. Here, we demonstrate a device-independent self-test protocol for this. We further establish an analytic noise-robust self-test. For a Bell-score deficit ε, we derive explicit O(ε) vector-norm bounds for the state and the corresponding measurement actions.
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.
We present a hitherto unexplored semi-device-independent (SDI) self-testing protocol designed to certify unitary operations within a variant of prepare-measure framework. We consider a communication game which we refer to as a variant of 3-bit prepare-measure random access code (PMRAC) involving two parties, Alice and Bob, who share a prior two-qubit quantum state. Alice encodes her message by applying unitary operations on her subsystem and sends it to Bob. To decode the message, Bob performs a measurement on the whole system. We demonstrate that the optimal quantum advantage of the variant of 3-bit PMRAC over the classical bound enables the self-testing of Alice's unitary operations and Bob's measurements. The derivation of the optimal quantum success probability is fully analytical. The approach is so elegant that it can be generalized for any arbitrary n-bit PMRAC and may also be extended to other prepare-measure communication games.
Self-testing is a phenomenon where the use of specific quantum states or measurements can be inferred solely from the correlations they generate. We introduce a universal method for conducting robustness analysis in the self-testing of various quantum resources. Unlike previous numerical approaches, which rely on selecting specific isometries, our method optimizes over equivalence transformations, thereby leading to tighter robustness bounds. This optimization employs the well-established technique of semidefinite programming relaxations for non-commuting polynomial optimization. Our method can be universally applied to diverse self-testing settings, including steerable assemblages in the Bell scenario, constellations of quantum states in the prepare-and-measure scenario, and entangled states in the steering scenario. We demonstrate the method's capability to surpass previously reported robustness bounds across a range of concrete examples.