Maximally entangled states are a key resource in many quantum communication and computation tasks, and their certification is a crucial element to guarantee the desired functionality. We introduce collective strategies for the efficient, local verification of ensembles of Bell pairs that make use of an initial information and noise transfer to few copies prior to their measurement. In this way the number of entangled pairs that need to be measured and hence destroyed is significantly reduced as compared to previous, even optimal, approaches that operate on individual copies. Moreover, the remaining states are directly certified. We show that our tools can be extended to other problems and larger classes of multipartite states.
Maximally entangled states are a key resource in many quantum communication and computation tasks, and their certification is a crucial element to guarantee the desired functionality. We introduce collective strategies for the efficient, local verification of ensembles of Bell pairs that make use of an initial information and noise transfer to few copies prior to their measurement. In this way the number of entangled pairs that need to be measured and hence destroyed is significantly reduced as compared to previous, even optimal, approaches that operate on individual copies. Moreover, the remaining states are directly certified. We show that our tools can be extended to other problems and larger classes of multipartite states.
We consider the quantum memory assisted quantum state verification task, where an adversary prepares independent multipartite entangled states and sends them to the local verifiers, who then store several copies in the quantum memory and measure them collectively to make a decision. We establish an exact analytic formula for optimizing two-copy state verification, where the verifiers store two copies, and give a globally optimal two-copy strategy for multiqubit graph states involving only Bell measurements. When the verifiers can store arbitrarily many copies, we present a dimension expansion technique that designs efficient verification strategies for this case, showcasing its application to efficiently verifying Greenberger-Horne-Zeilinger (GHZ)-like states. These strategies become increasingly advantageous with growing memory resources, ultimately approaching the theoretical limit of efficiency. Our findings demonstrate that quantum memories enhance state verification efficiency, shedding light on error-resistant strategies and practical applications of large-scale quantum memory assisted verification.
Assessing the quality of an ensemble of noisy entangled states is a central task in quantum information processing. Usually, this is done by measuring and hence destroying multiple copies, from which state tomography or fidelity estimation can be employed to characterize states. Here we propose several methods to directly distinguish between two different sets of states, e.g., if their fidelity is above or below a certain threshold value. This turns out to be significantly more efficient and importantly keeps the verified states intact. We make use of auxiliary entanglement or an ensemble of larger size, where we operate on the whole ensemble, but measure only a small fraction where information has been concentrated. For certain state families, we demonstrate that such an approach can even outperform optimal methods that collectively measure directly a fixed fraction of the ensemble.
Entangled quantum states are essential ingredients for many quantum technologies, but they must be validated before they are used. As a full characterization is prohibitively resource intensive, recent work has focused on developing methods to efficiently extract a few parameters of interest, in a so-called verification framework. Most existing approaches are based on preparing an ensemble of nominally identical and independently distributed (IID) quantum states and then measuring each copy of the ensemble. However, this leaves no states left for the intended quantum tasks and the IID assumptions do not always hold experimentally. To overcome these challenges, we experimentally implement quantum state certification (QSC), which measures only a subset of the ensemble, certifying the fidelity of multiple copies of the remaining states. We use active optical switches to randomly sample from sources of two-photon Bell states and three-photon GHZ (Greenberger-Horn-Zeilinger) states, reporting statistically sound fidelities in real time without destroying the entire ensemble. In addition, our QSC protocol removes the assumption that the states are identically distributed (but still assumes independent copies); can achieve close N −1 scaling, in the number of states measured N ; and can be implemented in a device-independent manner. Together, these benefits make our QSC protocol suitable for benchmarking large-scale quantum computing devices and deployed quantum communication setups relying on entanglement in both standard and adversarial situations.
Abstract The efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.
Abstract Quantum state verification (QSV) is the task of relying on local measurements only to verify that a given quantum device does produce the desired target state. Up to now, certain types of entangled states can be verified efficiently or even optimally by QSV. However, given an arbitrary entangled state, how to design its verification protocol remains an open problem. This study presents a systematic strategy to tackle this problem by considering the locality of what it initiates as the choice‐independent measurement protocols, whose operators can be directly achieved when they are homogeneous. Taking several typical entangled states as examples, this study shows the explicit procedures of the protocol design using standard Pauli projections, demonstrating the superiority of the method for attaining better QSV strategies. Moreover, the framework can be naturally extended to other tasks such as the construction of entanglement witnesses, and even parameter estimation.
In this work, we consider the fundamental task of quantum state certification: given copies of an unknown quantum state ρ, test whether it matches some target state σ or is ε-far from it. For certifying d-dimensional states, Θ(d/ε2) copies of ρ are known to be necessary and sufficient. However, the algorithm achieving this complexity makes fully entangled measurements over all O(d/ε2) copies of ρ. Often, one is interested in certifying states to a high precision; this makes such joint measurements intractable even for low-dimensional states. Thus, we study whether one can obtain optimal rates for quantum state certification and related testing problems while only performing measurements on t copies at once, for some 1<t≪d/ε2. While it is well-understood how to use intermediate entanglement to achieve optimal quantum state learning, the only protocol known to achieve optimal testing is the one using fully entangled measurements.
Our main result is a smooth copy complexity upper bound for state certification as a function of t, which achieves a near-optimal rate at t=d2. In the high-precision regime, i.e., for ε<d1, this is a strict improvement over the entanglement used by the aforementioned optimal protocol. We also extend our techniques to develop new algorithms for the related tasks of mixedness testing and purity estimation, and show tradeoffs achieving the optimal rates for these problems at t=d2 as well. Our algorithms are based on novel reductions from testing to learning and leverage recent advances in quantum state tomography in a non-black-box fashion. We complement our testing upper bounds with a (nearly) matching lower bound that holds in the high-precision regime, implying that one must take t≥Ω(d2) to achieve the optimal rate for certification.