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arXiv:2011.02216 · Nature Communications

Analysis and optimization of quantum adaptive measurement protocols with the framework of preparation games

Mirjam Weilenmann, Edgar A. Aguilar, Miguel Navascués

Published Jul 27, 2021• 9 citations
arXivHTMLPDF

Abstract

A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. Many experimental tasks in quantum information, such as entanglement quantification or magic state detection, can be cast as preparation games. In this paper, we introduce general methods to design n-round preparation games, with tight bounds on the performance achievable by players with arbitrarily constrained preparation devices. We illustrate our results by devising new adaptive measurement protocols for entanglement detection and quantification. Surprisingly, we find that the standard procedure in entanglement detection, namely, estimating n times the average value of a given entanglement witness, is in general suboptimal for detecting the entanglement of a specific quantum state. On the contrary, there exist n-round experimental scenarios where detecting the entanglement of a known state optimally requires adaptive measurement schemes.

DOI
10.1038/s41467-021-24658-9

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A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. Many experimental tasks in quantum information, such as entanglement quantification or magic state detection, can be cast as preparation games. In this paper, we introduce general methods to design n-round preparation games, with tight bounds on the performance achievable by players with arbitrarily constrained preparation devices. We illustrate our results by devising new adaptive measurement protocols for entanglement detection and quantification. Surprisingly, we find that the standard procedure in entanglement detection, namely, estimating n times the average value of a given entanglement witness, is in general suboptimal for detecting the entanglement of a specific quantum state. On the contrary, there exist n-round experimental scenarios where detecting the entanglement of a known state optimally requires adaptive measurement schemes.
Communication games are collaborative information processing tasks involving a number of players with limited communication. Such games are useful tools for studying physical theories. A physical theory exhibits preparation contextuality whenever observed behaviour cannot be explained by a preparation noncontextual model. Here we show that there is a fundamental connection between the performance in communication games and the degree of preparation (non)contextuality. For this purpose, we present a general framework that allows us to construct communication games such that the game performance corresponds to a measure of preparation (non)contextuality. We illustrate the power of this framework by, 1) deriving many examples of tests of preparation contextuality, 2) showing that quantum violations of Bell inequalities can be derived from quantum violations of preparation noncontextuality, 3) qualitatively and quantitatively explaining related previous results on preparation contextuality in quantum communication games, and 4) solving the open problem of revealing the preparation contextuality of the maximally mixed quantum state in any dimension.
Entanglement is one of the most fascinating features of quantum theory, as it fundamentally distinguishes quantum systems from classical systems. It not only might play a role in natural processes, but provides an especially powerful resource for a plethora of quantum information protocols, including quantum state teleportation, superdense coding as well as quantum computation schemes. However, for larger systems involving more than two parties, it is a challenging task to verify and characterize entanglement. In this thesis, efficient means for detecting genuine multipartite entanglement in multiqubit quantum systems will be derived, demonstrated, and discussed. Beyond that, methods for quantum state and process tomography will be introduced, which allow to analyze and investigate prepared multipartite states or even the performance of whole setups. Some typical obstacles for reliable state tomography will be pointed out, together with new means to understand experimentally obtained data. Finally, the measurement problem, which describes the unavoidable backaction of a measurement process to the quantum state under investigation, will be illustrated. Together with the discussion of different methods of quantum measurements, the optimal measurement instruments for binary qubit measurements will be derived. These optimal measurement instruments allow to perform a quantum measurement, providing a tunable amount of information about the quantum state, while avoiding any unnecessary disturbance to the state. This set of optimal instruments will be compared to other measurement schemes, such as measurements based on the optimal quantum cloning protocol.
Abstract We present a self-testing protocol in a constrained prepare-measure scenario, based on a communication game known as parity-oblivious multiplexing (POM) task. In this scenario, a parity-oblivious constraint is imposed on the preparations, allowing us to define a classical bound derived from a preparation noncontextual ontological model. We demonstrate that the optimal quantum value exceeds preparation noncontextual bound and therefore enables self-testing of the preparations and the measurement devices. Contrasting the prevailing consensus that the self-testing in prepare-measure scenario inevitably requires an upper bound on the dimension of the quantum system, we derive the optimal quantum success probability of the POM task devoid of assuming the dimension of the quantum system. Furthermore, by proving the existence of a unitary, we show that the optimal preparations and measurements in an unknown but finite dimensional Hilbert space, responsible for the observed input–output correlations, can be mapped, via a unitary, onto a known finite-dimensional quantum system. Our results thus pave the way for scalable, single system based certification protocols in the prepare-measure scenario.
Quantum metrology studies the use of quantum mechanical systems as measurement devices or sensors. Surprisingly, preparing a sensor in an entangled state can enhance measurement precision. The simplest protocols for entanglement enhancement sense only small changes in a quantity. The range of values over which a measurement protocol works is called its dynamic range. For many types of sensors we require end-to-end protocols that describe how to use entanglement to achieve enhanced precision over a large dynamic range. In this dissertation, we describe two approaches to achieving entanglement-enhanced sensing over a large dynamic range. The first approach uses entangling resources in a way that circumvents the dynamic-range limitation by numerically optimizing variational circuits. Our protocols show improved performance at fixed circuit depth compared to previous variational-circuit-based approaches, and the generality of our approach reveals several generic features of such protocols. The second approach uses adaptivity to first obtain a preliminary estimate of the quantity and then iteratively refines it. In particular, we describe the use of one-axis twisting dynamics at each stage of this protocol to minimize the expected estimation error.
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.
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through adaptive measurements, computing the maximum average score of a preparation game over a continuous set of target states, and limiting the behavior of a (quantum) finite-state automaton. In this work, we introduce tractable relaxations of this class of optimization problems. To illustrate their performance, we use them to: (a) compute the probability that a finite-state automaton outputs a given sequence of bits; (b) develop a new many-body entanglement-detection protocol; and (c) let the computer an adaptive protocol for magic state detection. As we further show, the maximum score of a sequential problem in the limit of infinitely many time steps is in general incomputable. Nonetheless, we provide general heuristics to bound this quantity and show that they provide useful estimates in relevant scenarios. Published by the American Physical Society 2024