In the development of quantum technologies, a reliable means for characterizing quantum devices, be it a measurement device, a state-preparation device, or a transformation device, is crucial. However, the conventional approach based on, for example, quantum state tomography or process tomography relies on assumptions that are often not necessarily justifiable in a realistic experimental setting. Although the device-independent (DI) approach to this problem bypasses the shortcomings above by making only minimal, justifiable assumptions, most of the theoretical proposals to date only work in the idealized setting where independent and identically distributed (i.i.d.) trials are assumed. Here, we provide a versatile solution for rigorous device-independent certification that does not rely on the i.i.d. assumption. Specifically, we describe how the prediction-based ratio (PBR) protocol and martingale-based protocol developed for hypothesis testing can be applied in the present context to achieve a device-independent certification of desirable properties with confidence interval (CI). To illustrate the versatility of these methods, we demonstrate how we can use them to certify—with finite data—the underlying negativity, Hilbert space dimension, entanglement depth, and fidelity to some target pure state. In particular, we provide examples showing how the amount of certifiable negativity and fidelity scales with the number of trials and how many experimental trials one needs to certify a qutrit state space or the presence of genuine tripartite entanglement. Overall, we have found that the PBR protocol and the martingale-based protocol often offer similar performance, even though the latter does have to presuppose any witness (Bell-like inequality). In contrast, our findings also show that the performance of the martingale-based protocol may be severely affected by one’s choice of Bell-like inequality. Intriguingly, a Bell function useful for self-testing does not necessarily give the optimal confidence-gain rate for certifying the fidelity to the corresponding target state.
In the development of quantum technologies, a reliable means for characterizing quantum devices, be it a measurement device, a state-preparation device, or a transformation device, is crucial. However, the conventional approach based on, for example, quantum state tomography or process tomography relies on assumptions that are often not necessarily justifiable in a realistic experimental setting. Although the device-independent (DI) approach to this problem bypasses the shortcomings above by making only minimal, justifiable assumptions, most of the theoretical proposals to date only work in the idealized setting where independent and identically distributed (i.i.d.) trials are assumed. Here, we provide a versatile solution for rigorous device-independent certification that does not rely on the i.i.d. assumption. Specifically, we describe how the prediction-based ratio (PBR) protocol and martingale-based protocol developed for hypothesis testing can be applied in the present context to achieve a device-independent certification of desirable properties with confidence interval (CI). To illustrate the versatility of these methods, we demonstrate how we can use them to certify—with finite data—the underlying negativity, Hilbert space dimension, entanglement depth, and fidelity to some target pure state. In particular, we provide examples showing how the amount of certifiable negativity and fidelity scales with the number of trials and how many experimental trials one needs to certify a qutrit state space or the presence of genuine tripartite entanglement. Overall, we have found that the PBR protocol and the martingale-based protocol often offer similar performance, even though the latter does have to presuppose any witness (Bell-like inequality). In contrast, our findings also show that the performance of the martingale-based protocol may be severely affected by one’s choice of Bell-like inequality. Intriguingly, a Bell function useful for self-testing does not necessarily give the optimal confidence-gain rate for certifying the fidelity to the corresponding target state.
Standard quantum verification and certification protocols often assume that experimental sources emit independent and identically distributed (i.i.d.) states. In realistic scenarios, however, temporal drift, memory effects, feedback, and correlated noise can violate this assumption, causing standard analyses to underestimate uncertainty and overestimate device performance. Here, we introduce a general framework for quantum verification and certification in which the state produced in each round may depend arbitrarily on the preceding experimental history. Our method provides rigorous confidence intervals for observable expectation values averaged over the experimental trajectory. The framework covers both full verification, in which every state is measured, and spot-checking certification, in which a randomly selected subset is tested to certify the average observable value of the complementary, remaining systems. We apply the framework to importance-sampled Pauli measurements for direct fidelity estimation, energy estimation, and entanglement witnessing, and to classical shadows, allowing multiple observables to be certified simultaneously from the same test data. We illustrate the framework numerically and demonstrate it experimentally through Bell-state certification on a quantum processor.
Self-testing is a method to certify devices from the result of a Bell test. Although examples of noise tolerant self-testing are known, it is not clear how to deal efficiently with a finite number of experimental trials to certify the average quality of a device without assuming that it behaves identically at each run. As a result, existing self-testing results with finite statistics have been limited to guarantee the proper working of a device in just one of all experimental trials, thereby limiting their practical applicability. We here derive a method to certify through self-testing that a device produces states on average close to a Bell state without assumption on the actual state at each run. Thus the method is free of the I.I.D. (independent and identically distributed) assumption. Applying this new analysis on the data from a recent loophole-free Bell experiment, we demonstrate the successful distribution of Bell states over 398 meters with an average fidelity of ≥ 55.50% at a confidence level of 99%. Being based on a Bell test free of detection and locality loopholes, our certification is evidently device-independent, that is, it does not rely on trust in the devices or knowledge of how the devices work. This guarantees that our link can be integrated in a quantum network for performing long-distance quantum communications with security guarantees that are independent of the details of the actual implementation.
Abstract In quantum information, device-independent (DI) protocols offer a new approach to information processing tasks, making minimal assumptions about the devices used. Typically, since these protocols draw conclusions directly from the data collected in a meaningful Bell test, the no-signaling conditions, and often even Born’s rule for local measurements, are taken as premises of the protocol. Here, we demonstrate how to test such premises in an (almost) DI setting, i.e. directly from the raw data and with minimal assumptions. In particular, for IBM’s quantum computing cloud services, we implement the prediction-based ratio protocol to characterize how well the qubits can be accessed locally and independently. More precisely, by performing a variety of Clauser–Horne–Shimony–Holt-type experiments on these systems and carrying out rigorous hypothesis tests on the collected data, we provide compelling evidence showing that some of these qubits suffer from measurement cross-talks, i.e. their measurement statistics are affected by the choice of measurement bases on another qubit. Unlike standard randomized benchmarking, our approach does not rely on assumptions such as gate-independent Markovian noise. Moreover, despite the relatively small number of experimental trials, the direction of ‘signaling’ may also be identified in some cases. Our approach thus serves as a complementary tool for benchmarking the local addressability of quantum computing devices.
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.
Certifying a quantum state in a device-independent (DI) manner, in which no trust is placed on the internal workings of any physical components, is a fundamental task bearing various applications in quantum information theory. The composability of a state-certification protocol is key to its integration as a subroutine within information-theoretic protocols. In this work, we present a composable certification of quantum states in a DI manner under the assumption that a source prepares a finite sequence of independent quantum states that are not necessarily identical. We show that the security relies on the DI analog of the fidelity, called the . We develop methods to compute this quantity under local operations and classical communication in certain Bell scenarios that self-test the singlet state, which may also be of independent interest. Finally, we demonstrate our framework by certifying the singlet state in a composable and DI manner using the Clauser-Horne-Shimony-Holt inequality.
The device-independent approach to physics is one where conclusions are drawn directly and solely from the observed correlations between measurement outcomes. In quantum information, this approach allows one to make strong statements about the properties of the underlying devices via the observation of Bell-inequality-violating correlations. However, since one can only perform a finite number of experimental trials, an important gap remains between the many theoretical tools developed for such purposes and the experimentally obtained raw data. In particular, a sensible way to estimate the underlying quantum distribution has so far remained elusive. Here, we propose a few methods to bridge this gap. Under the assumption that the experimental trials are independent and identically distributed, our methods allow one to achieve the analog of quantum state estimation in the device-independent setting by generating unique point estimates of the true quantum distribution. In addition, we provide strong numerical evidence showing that these estimates converge toward the underlying distribution with a rate at least as good as the relative frequencies. We further demonstrate how these estimates of the true quantum distribution can be used to provide sensible estimates of certain desired properties of the system, such as the amount of entanglement present in the measured system.