In practical situations, the reliability of quantum resources can be compromised due to complex generation processes or adversarial manipulations during transmission. Consequently, the trials generated sequentially in an experiment may exhibit non-independent and non-identically distributed (non-i.i.d.) behavior. This non-i.i.d. behavior can introduce security concerns and result in faulty estimates when performing information tasks such as quantum key distribution, self-testing, verifiable quantum computation, and resource allocation in quantum networks. To certify the performance of such tasks, one can make a random decision in each trial, either spot-checking some desired property or utilizing the quantum resource for the given task. However, a general method for certification with a sequence of non-i.i.d. spot-checking trials is still missing. Here, we develop such a method. This method not only works efficiently with a finite number of trials but also yields asymptotically tight certificates of performance. Our analysis shows that even as the total number of trials approaches infinity, only a constant number of trials needs to be spot-checked on average to certify the average performance of the remaining trials at a specified confidence level.
In practical situations, the reliability of quantum resources can be compromised due to complex generation processes or adversarial manipulations during transmission. Consequently, the trials generated sequentially in an experiment may exhibit non-independent and non-identically distributed (non-i.i.d.) behavior. This non-i.i.d. behavior can introduce security concerns and result in faulty estimates when performing information tasks such as quantum key distribution, self-testing, verifiable quantum computation, and resource allocation in quantum networks. To certify the performance of such tasks, one can make a random decision in each trial, either spot-checking some desired property or utilizing the quantum resource for the given task. However, a general method for certification with a sequence of non-i.i.d. spot-checking trials is still missing. Here, we develop such a method. This method not only works efficiently with a finite number of trials but also yields asymptotically tight certificates of performance. Our analysis shows that even as the total number of trials approaches infinity, only a constant number of trials needs to be spot-checked on average to certify the average performance of the remaining trials at a specified confidence level.
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.
For practical applications of quantum randomness generation, it is important to certify and further produce a fixed block of fresh random bits with as few trials as possible.Consequently, protocols with high finite-data efficiency are preferred.To yield such protocols with respect to quantum side information, we develop quantum probability estimation.Our approach is applicable to device-independent as well as device-dependent scenarios, and it generalizes techniques from previous works [Miller and Shi, SIAM J. Comput. 46, 1304 (2017); Arnon-Friedman et al., Nat. Commun. 9, 459 (2018)].Quantum probability estimation can adapt to changing experimental conditions, allows stopping the experiment as soon as the prespecified randomness goal is achieved, and can tolerate imperfect knowledge of the input distribution.Moreover, the randomness rate achieved at constant error is asymptotically optimal.For the device-independent scenario, our approach certifies the amount of randomness available in experimental results without first searching for relations between randomness and violations of fixed Bell inequalities.We implement quantum probability estimation for device-independent randomness generation in the CHSH Bell-test configuration, and we show significant improvements in finite-data efficiency, particularly at small Bell violations which are typical in current photonic loophole-free Bell tests.
Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing.Steady progress vis-à-vis verification of quantum devices in the scenario with fully characterized measurement devices has been observed in recent years.When it comes to the scenario with uncharacterized measurements, the so-called black-box scenario, practical verification methods are still rather scarce.Development of self-testing methods is an important step forward, but these results so far have been used for reliable verification only by considering the asymptotic behavior of large, identically and independently distributed (IID) samples of a quantum resource.Such strong assumptions deprive the verification procedure of its truly device-independent character.In this paper, we develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime.Remarkably, we show that device-independent verification can be performed with optimal sample efficiency.Finally, for the case of independent copies, we develop a device-independent protocol for quantum state certification: a protocol in which a fragment of the resource copies is measured to warrant the rest of the copies to be close to some target state.
Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the context of semi-device-independent randomness certification using sequential maximum-confidence measurements. We develop a general framework and versatile numerical methods to bound the amount of certifiable randomness in such scenarios. We further introduce a technique to compute min-tradeoff functions via semidefinite programming duality, thus making the framework suitable for bounding the certifiable randomness against adaptive attacking strategies through entropy accumulation. Our results establish sufficient criteria showing that maximum-confidence measurements enable the distribution and certification of randomness across a sequential measurement chain in single-party systems.
The certification of quantum resources is a critical tool in the development of quantum information processing. In particular, quantum state verification is a fundamental building block for communication and computation applications, determining whether the involved parties can trust the resources at hand or whether the application should be aborted. Self-testing methods have been used to tackle such verification tasks in a device-independent (DI) setting. However, these approaches commonly consider the limit of large (asymptotic), independent and identically distributed (IID) samples, which weakens the DI claim and poses serious challenges to their experimental implementation. Here, we overcome these challenges by adopting a theoretical protocol, enabling the certification of quantum states in the few-copies and non-IID regime and by leveraging a high-fidelity multipartite entangled photon source. This allows us to show the efficient and DI certification of a single copy of a four-qubit GHZ state that can readily be used for the robust and reliable implementation of quantum information tasks.
The certification of quantum resources is a critical tool in the development of quantum information processing. In particular, quantum state verification is a fundamental building block for communication and computation applications, determining whether the involved parties can trust the resources at hand or whether the application should be aborted. Self-testing methods have been used to tackle such verification tasks in a device-independent (DI) setting. However, these approaches commonly consider the limit of large (asymptotic), independent and identically distributed (IID) samples, which weakens the DI claim and poses serious challenges to their experimental implementation. Here, we overcome these challenges by adopting a theoretical protocol, enabling the certification of quantum states in the few-copies and non-IID regime and by leveraging a high-fidelity multipartite entangled photon source. This allows us to show the efficient and DI certification of a single copy of a four-qubit GHZ state that can readily be used for the robust and reliable implementation of quantum information tasks.