This paper explores an efficient method for entanglement quantification in two-qubit and qubit-qutrit quantum systems based upon the framework of collective measurements in conjunction with machine learning. We introduce an adaptive measurement procedure in which measurement settings are dynamically adjusted based on prior measurement outcomes aiming to optimize the inference precision given a limited number of these measurement settings. The procedure makes use of the Long Short-Term Memory networks to recurrently process collective measurements on two copies of the investigated states. Obtained results demonstrate the tangible benefits of the adaptive measurements in comparison to previously described non-adaptive strategies.
This paper explores an efficient method for entanglement quantification in two-qubit and qubit-qutrit quantum systems based upon the framework of collective measurements in conjunction with machine learning. We introduce an adaptive measurement procedure in which measurement settings are dynamically adjusted based on prior measurement outcomes aiming to optimize the inference precision given a limited number of these measurement settings. The procedure makes use of the Long Short-Term Memory networks to recurrently process collective measurements on two copies of the investigated states. Obtained results demonstrate the tangible benefits of the adaptive measurements in comparison to previously described non-adaptive strategies.
In this paper, we introduce a supervised learning technique that harnesses artificial neural networks, along with the outcomes of collective entanglement measurements, to estimate the negativity of quantum states in two-qubit and qubit-qutrit systems. The resulting deep-learned collective entanglement witnesses offer the unique capability of continuous sensitivity and selectivity tuning. This instrument enables us to explore the tradeoff between sensitivity and selectivity in entanglement detection, a dimension not accessible to previously employed analytical witnesses. In particular, we demonstrate that there are experimentally cost-effective methods (in terms of the number of measurements) where sensitivity can be significantly improved at a slight expense of the selectivity of entanglement detection. This chosen approach is also favored due to its high generality and potential for superior performance compared to other types of entanglement witnesses. Our findings may pave the way for the development of more efficient and accurate entanglement detection methods in complex quantum systems, especially when considering realistic experimental imperfections. Published by the American Physical Society 2024
Abstract The recently established resource theory of quantum coherence allows for a quantitative understanding of the superposition principle, with applications reaching from quantum computing to quantum biology. While different quantifiers of coherence have been proposed in the literature, their efficient estimation in today’s experiments remains a challenge. Here, we introduce a collective measurement scheme for estimating the amount of coherence in quantum states, which requires entangled measurements on two copies of the state. As we show by numerical simulations, our scheme outperforms other estimation methods based on tomography or adaptive measurements, leading to a higher precision in a large parameter range for estimating established coherence quantifiers of qubit and qutrit states. We show that our method is accessible with today’s technology by implementing it experimentally with photons, finding a good agreement between experiment and theory.
Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply RLNN to quantum hypothesis testing and determine the optimal measurement strategy for distinguishing between multiple quantum states {ρj} while minimizing the error probability. In the case where the candidate states correspond to a quantum system with many qubit subsystems, implementing the optimal measurement on the entire system is experimentally infeasible. We use RLNN to find locally-adaptive measurement strategies that are experimentally feasible, where only one quantum subsystem is measured in each round. We provide numerical results which demonstrate that RLNN successfully finds the optimal local approach, even for candidate states up to 20 subsystems. We additionally demonstrate that the RLNN strategy meets or exceeds the success probability for a modified locally greedy approach in each random trial.While the use of RLNN is highly successful for designing adaptive local measurement strategies, in general a significant gap can exist between the success probability of the optimal locally-adaptive measurement strategy and the optimal collective measurement. We build on previous work to provide a set of necessary and sufficient conditions for collective protocols to strictly outperform locally adaptive protocols. We also provide a new example which, to our knowledge, is the simplest known state set exhibiting a significant gap between local and collective protocols. This result raises interesting new questions about the gap between theoretically optimal measurement strategies and practically implementable measurement strategies.
Quantum entanglement, a bizarre phenomenon where two or more particles become linked in such a way that they share the same fate, holds immense potential for technological advancement. This paper investigates the application of quantum entanglement to the design of an adaptive measurement algorithm, aiming to enhance measurement precision and efficiency. Traditional measurement techniques often rely on fixed parameters, limiting their ability to optimize performance. We propose a novel approach leveraging the dynamic interplay between entangled states and adjustable parameters to achieve this. The core mechanism centers around exploiting the inherent correlations within entangled systems to dynamically adjust measurement settings, resulting in improved accuracy and reduced computational burden. This research explores the theoretical and practical aspects of this algorithm, emphasizing its potential impact on various measurement scenarios.
In this work, we consider the fundamental task of estimating the purity of an unknown state to within multiplicative error ε. When one can perform general collective measurements, Θ(ε2d+εd) copies are known to be necessary and sufficient for this problem [AISW20]. However, implementing collective measurements on such a large number of copies can be experimentally demanding, and we thus aim to characterize the copy complexity of this problem with incoherent measurements.
In this setting, the only non-trivial result is a non-adaptive algorithm that uses O(ε2d+εd2) copies [PTTW26], which is polynomially larger than the best-known lower bound. Our first result is a new algorithm performing non-adaptive incoherent measurements that succeeds using O(ε2d+εd3/2) copies, improving on the latter term in the copy complexity. Moreover, we show that for any algorithm restricted to non-adaptive measurements, the above copy complexity is optimal.
We also develop a new adaptive estimator for the purity of a state that improves on the above complexity in the high-precision regime, i.e., for ε=o(1/d). We also show that the non-adaptive and adaptive estimators together yield the optimal complexity for incoherent purity estimation; in particular, we show that the copy complexity of this problem is Θ(min{ε2d+εd3/2,εd2+ε2d}).
Current algorithms for quantum state tomography (QST) are costly both on the experimental front, requiring measurement of many copies of the state, and on the classical computational front, needing a long time to analyze the gathered data. Here, we introduce neural adaptive quantum state tomography (NAQT), a fast, flexible machine-learning-based algorithm for QST that adapts measurements and provides orders of magnitude faster processing while retaining state-of-the-art reconstruction accuracy. As in other adaptive QST schemes, measurement adaptation makes use of the information gathered from previous measured copies of the state to perform a targeted sensing of the next copy, maximizing the information gathered from that next copy. Our NAQT approach allows for a rapid and seamless integration of measurement adaptation and statistical inference, using a neural-network replacement of the standard Bayes’ update, to obtain the best estimate of the state. Our algorithm, which falls into the machine learning subfield of “meta-learning” (in effect “learning to learn” about quantum states), does not require any ansatz about the form of the state to be estimated. Despite this generality, it can be retrained within hours on a single laptop for a two-qubit situation, which suggests a feasible time-cost when extended to larger systems and potential speed-ups if provided with additional structure, such as a state ansatz.