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Optics Express

Extracting information from single qubits among multiple observers with optimal weak measurements

Xing-Xiang Peng, Peng Yin, Wen-Hao Zhang, Gongchu Li, De‐Yong He, Xiao-Ye Xu, Jin‐Shi Xu, Geng Chen, Chuan‐Feng Li, Guang‐Can Guo

Published Jun 15, 2020• 2 citations
Publisher

Abstract

In the context of quantum information, major efforts have been made to maximize the mutual information by measuring single copies of signal states. In general, one execution of optimal projective measurement extracts all the accessible mutual information. However, in some scenarios, weak measurements are preferred because of kinds of specific requirements, e.g., to distribute secret keys to multi-observers. In this study, we propose a method to construct optimal weak measurements for multi-party quantum communications. Utilizing the method in [Physical Review Letters 120, 160501 (2018)] to classify the mutual information, the theoretical study shows that by successively performing this optimal weak measurement, all accessible information can be obtained by multiple observers. This conclusion is experimentally verified by a cascaded measurement apparatus that can perform six successive weak measurements on heralded single photons. The experimental results clearly indicate that almost all accessible mutual information is extracted by this sequence of optimal weak measurements; meanwhile, none of the information is destroyed or residual. Thus, this optimal weak measurement is an efficient and reliable tool for performing quantum communication tasks. The consistence between the experimental and theoretical results verifies that the classifying method in [Phys. Rev. Lett.120, 160501 (2018)] can be applied to characterize realistic quantum measurements.

DOI
10.1364/oe.395033

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In the context of quantum information, major efforts have been made to maximize the mutual information by measuring single copies of signal states. In general, one execution of optimal projective measurement extracts all the accessible mutual information. However, in some scenarios, weak measurements are preferred because of kinds of specific requirements, e.g., to distribute secret keys to multi-observers. In this study, we propose a method to construct optimal weak measurements for multi-party quantum communications. Utilizing the method in [Physical Review Letters 120, 160501 (2018)] to classify the mutual information, the theoretical study shows that by successively performing this optimal weak measurement, all accessible information can be obtained by multiple observers. This conclusion is experimentally verified by a cascaded measurement apparatus that can perform six successive weak measurements on heralded single photons. The experimental results clearly indicate that almost all accessible mutual information is extracted by this sequence of optimal weak measurements; meanwhile, none of the information is destroyed or residual. Thus, this optimal weak measurement is an efficient and reliable tool for performing quantum communication tasks. The consistence between the experimental and theoretical results verifies that the classifying method in [Phys. Rev. Lett.120, 160501 (2018)] can be applied to characterize realistic quantum measurements.
Quantum information processing and computation requires high accuracy qubit configuration readout. In many practical schemes, the initial qubit configuration has to be inferred from readout that is a time-dependent weak measurement record. However, a combination of the measurement scheme and intrinsic dynamics can end up scrambling the initial state and lose information irretrievably. Here, we study the information physics of quantum trajectories based on weak measurements in order to address the optimal achievable performance in qubit configuration readout for two realistic models of single qubit readout: (i) Model I is informationally complete, but without intrinsic dynamics; (ii) Model II is informationally incomplete weak measurements with intrinsic dynamics. We first use mutual information to characterize how much intrinsic information about the initial state is encoded in the measurement record. Using a fixed discrete time-step formulation, we compute the mutual information while varying the measurement strength, duration of measurement record, and the relative strength of intrinsic dynamics in our measurement schemes. We also exploit the emergence of continuum scaling and the Stochastic Master Equation in the weak measurement limit. We develop an asymptotic expansion in the measurement efficiency parameter to calculate mutual information, which captures qualitative and quantitative features of the numerical data. The bounds on information extraction are manifested as plateaux in mutual information, our analysis obtains these bounds and also optimal duration of measurement required to saturate them. Our results should be useful both for quantum device operation and optimization and also, possibly, for improving the performance of recent machine learning approaches for qubit and multiqubit configuration readout in current Noisy Intermediate-Scale Quantum (NISQ) experiment regimes.
Quantum detectors provide information about the microscopic properties of quantum systems by establishing correlations between those properties and a set of macroscopically distinct events that we observe. The question of how much information a quantum detector can extract from a system is therefore of fundamental significance. In this paper, we address this question within a precise framework: given a measurement apparatus implementing a specific POVM measurement, what is the optimal performance achievable with it for a specific information readout task and what is the optimal way to encode information in the quantum system in order to achieve this performance? We consider some of the most common information transmission tasks—the Bayes cost problem, unambiguous message discrimination and the maximal mutual information. We provide general solutions to the Bayesian and unambiguous discrimination problems. We also show that the maximal mutual information is equal to the classical capacity of the quantum-to-classical channel describing the measurement, and study its properties in certain special cases. For a group covariant measurement, we show that the problem is equivalent to the problem of accessible information of a group covariant ensemble of states. We give analytical proofs of optimality in some relevant cases. The framework presented here provides a natural way to characterize generalized quantum measurements in terms of their information readout capabilities.
Given an unknown state of a qudit that has already been measured optimally, can one still extract any information about the original unknown state? Clearly, after a maximally informative measurement, the state of the system collapses into a postmeasurement state from which the same observer cannot obtain further information about the original state of the system. However, the system still encodes a significant amount of information about the original preparation for a second observer who is unaware of the actions of the first one. We study how a series of independent observers can obtain, or can scavenge, information about the unknown state of a system (quantified by the fidelity) when they sequentially measure it. We give closed-form expressions for the estimation fidelity when one or several qudits are available to carry information about the single-qudit state, and we study the classical limit when an arbitrarily large number of observers can obtain (nearly) complete information on the system. In addition to the case where all observers perform most informative measurements, we study the scenario where a finite number of observers estimates the state with equal fidelity, regardless of their position in the measurement sequence and the scenario where all observers use identical measurement apparatuses (up to a mutually unknown orientation) chosen so that a particular observer's estimation fidelity is maximized.
Abstract Quantum communication has been leading the way of many remarkable theoretical results and experimental tests in physics. In this context, quantum communication complexity (QCC) has recently drawn earnest research attention as a tool to optimize the amounts of transmitted qubits and energy that are required to implement distributed computational tasks. On this matter, we introduce a novel multi-user quantum fingerprinting (QF) protocol that is ready to be implemented with existing technology. Particularly, we extend to the multi-user framework a well-known two-user coherent-state fingerprinting scheme. This generalization is highly non-trivial for a twofold reason, as it requires not only to extend the set of protocol rules but also to specify a procedure for designing the optical devices intended for the generalized protocol. Much of the importance of our work arises from the fact that the obtained QCC figures of merit allow direct comparison with the best-known classical multi-user fingerprinting protocol, of significance in the field of computer technologies and networking. Furthermore, as one of the main contributions of the manuscript, we deduce innovative analytical upper bounds on the amount of transmitted quantum information that are even valid in the two-user protocol as a particular case. These original analytical bounds are of interest for estimating the realistic protocol performance prior to experimental realizations. Ultimately, comparative results are provided to contrast different protocol implementation strategies and, importantly, to show that, under realistic circumstances, the multi-user protocol can achieve tasks that are impossible by using classical communication alone. Our work provides relevant contributions towards understanding the nature and the limitations of QF and, on a broader scope, also the limitations and possibilities of quantum-communication networks embracing a node that is accessed by multiple users at the same time.
Quantum correlation is a key resource for a variety of quantum information processing and communication tasks, the efficient utilization of which has been a longstanding concern, and it is also one of the main challenges in the application of quantum technology. In this review, we focus on the interaction between quantum measurements and quantum correlations by designing appropriate measurement strategies, specifically exploring the trade-off between information gain and disturbance degree in weak measurements to ensure that quantum correlations from the same source can be shared among multiple independent observers. We introduce the basic knowledge and classification of quantum measurements, investigate the weak measurement scenario, and show the theoretical model construction of quantum correlation recycling in the original works. We summarize the theoretical and experimental development process and the latest progress in this field. Finally, we provide an outlook for more quantum resource applications that can profit from the optimization of quantum measurement strategies.
We explore the use of weak quantum measurements for single-qubit quantum state tomography processes. Weak measurements are those where the coupling between the qubit and the measurement apparatus is weak; this results in the quantum state being disturbed less than in the case of a projective measurement. We employ a weak measurement tomography protocol developed by Das and Arvind, which they claim offers a new method of extracting information from quantum systems. We test the Das-Arvind scheme for various measurement strengths, and ensemble sizes, and reproduce their results using a sequential stochastic simulation. Lastly, we place these results in the context of current understanding of weak and projective measurements.