Self-testing allows classical referees to verify the quantum behaviour of some untrusted devices. Recently we developed a framework for building large self-tests by repeating a smaller self-test many times in parallel. However, the framework did not apply to the CHSH test, which tests a maximally entangled pair of qubits. CHSH is the most well known and widely used test of this type. Here we extend the parallel self-testing framework to build parallel CHSH self-tests for any number of pairs of maximally entangled qubits. Our construction achieves an error bound which is polynomial in the number of tested qubit pairs.
Self-testing allows classical referees to verify the quantum behaviour of some untrusted devices. Recently we developed a framework for building large self-tests by repeating a smaller self-test many times in parallel. However, the framework did not apply to the CHSH test, which tests a maximally entangled pair of qubits. CHSH is the most well known and widely used test of this type. Here we extend the parallel self-testing framework to build parallel CHSH self-tests for any number of pairs of maximally entangled qubits. Our construction achieves an error bound which is polynomial in the number of tested qubit pairs.
Self-testing allows us to determine, through classical interaction only, whether some players in a non-local game share particular quantum states. Most work on self-testing has concentrated on developing tests for small states like one pair of maximally entangled qubits, or on tests where there is a separate player for each qubit, as in a graph state. Here we consider the case of testing many maximally entangled pairs of qubits shared between two players. Previously such a test was shown where testing is sequential, i.e., one pair is tested at a time. Here we consider the parallel case where all pairs are tested simultaneously, giving considerably more power to dishonest players. We derive sufficient conditions for a self-test for many maximally entangled pairs of qubits shared between two players and also two constructions for self-tests where all pairs are tested simultaneously.
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.
Device-independent self-testing allows a verifier to certify that potentially malicious parties hold on to a specific quantum state, based only on the observed correlations. Parallel self-testing has recently been explored, aiming to self-test many copies (i.e. a tensor product) of the target state concurrently. In this work, we show that n EPR pairs can be self-tested in parallel through n copies of the well known CHSH game. We generalise this result further to a parallel self-test of n tilted EPR pairs with arbitrary angles, and finally we show how our results and calculations can also be applied to obtain a parallel self-test of 2n EPR pairs via n copies of the Mermin-Peres magic square game.
Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ε must be poly(N,ε)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.
Device-independent self-testing allows a verifier to certify that potentially malicious parties hold on to a specific quantum state, based only on the observed correlations. Parallel self-testing has recently been explored, aiming to self-test many copies (i.e. a tensor product) of the target state concurrently. In this work, we show that n EPR pairs can be self-tested in parallel through n copies of the well known CHSH game. We generalise this result further to a parallel self-test of n tilted EPR pairs with arbitrary angles, and finally we show how our results and calculations can also be applied to obtain a parallel self-test of 2n EPR pairs via n copies of the Mermin-Peres magic square game.
Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system's state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.