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arXiv:2405.11447

Disturbance Evaluation Circuit in Quantum Measurement

Haruki Emori, Masanao Ozawa, Akihisa Tomita

Published May 19, 2024• 0 citations
arXivHTMLPDF

Abstract

According to the uncertainty principle, every quantum measurement accompanies disturbance. In particular, accurate sequential measurements need the accurate control of disturbance. However, the correct role of disturbance in the uncertainty principle has been known only recently. Understanding the disturbance is crucial for understanding the fundamentals of physics, and accurately evaluating the disturbance is important for quantum technologies such as quantum information processing and quantum metrology. Therefore, the experimental evaluation of the disturbance is a significant challenge in those fields. In this study, we propose a novel evaluation method for the quantum root-mean-square (QRMS) disturbance and compare its performance with the existing approaches, known as the three-state method (TSM) and the weak measurement method (WMM). Our method establishes a correspondence between the QRMS disturbance of the measurement and the second-order derivative of the decoherence induced in a newly introduced weak probe system with respect to the coupling strength of the weak interaction at its zero-limit. Furthermore, we demonstrate the effectiveness of our method in comparison with the other two through a simulation and experiment using a quantum computer. The results capture the key features of the TSM, WMM, and our method, providing insights into the strengths and limitations of these methods.

DOI
10.48550/arxiv.2405.11447

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According to the uncertainty principle, every quantum measurement accompanies disturbance. In particular, accurate sequential measurements need the accurate control of disturbance. However, the correct role of disturbance in the uncertainty principle has been known only recently. Understanding the disturbance is crucial for understanding the fundamentals of physics, and accurately evaluating the disturbance is important for quantum technologies such as quantum information processing and quantum metrology. Therefore, the experimental evaluation of the disturbance is a significant challenge in those fields. In this study, we propose a novel evaluation method for the quantum root-mean-square (QRMS) disturbance and compare its performance with the existing approaches, known as the three-state method (TSM) and the weak measurement method (WMM). Our method establishes a correspondence between the QRMS disturbance of the measurement and the second-order derivative of the decoherence induced in a newly introduced weak probe system with respect to the coupling strength of the weak interaction at its zero-limit. Furthermore, we demonstrate the effectiveness of our method in comparison with the other two through a simulation and experiment using a quantum computer. The results capture the key features of the TSM, WMM, and our method, providing insights into the strengths and limitations of these methods.
One of the crucial tasks in quantum systems is to reduce the effects of decoherence due to the unavoidable interactions between a system and its environment. Many protection schemes have been proposed recently, among them the weak measurement quantum measurement reversal (WMQMR), weak measurement-based quantum feedback control (QFBC) and quantum feedforward control (QFFC) are reviewed in this paper. By considering weak measurement, the aim is to find a balance between information gain and disturbance of the system caused by the measurement. We classify different types of measurement and give the definition of noise sources and their effects on the state of the system. Finally, we compare and analyze the performance of the discussed protection schemes for different noise sources by numerical simulations.
A goal of the emerging field of quantum control is to develop methods for quantum technologies to function robustly in the presence of noise. Central issues are the fundamental limitations on the available information about quantum systems and the disturbance they suffer in the process of measurement. In the context of a simple quantum control scenario-the stabilization of nonorthogonal states of a qubit against dephasing-we experimentally explore the use of weak measurements in feedback control. We find that, despite the intrinsic difficultly of implementing them, weak measurements allow us to control the qubit better in practice than is even theoretically possible without them. Our work shows that these more general quantum measurements can play an important role for feedback control of quantum systems.
Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here the conflict is resolved by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics. Two approaches to adapting the classic notion of root-mean-square error to quantum measurements are discussed. One is based on the concept of a noise operator; its natural operational content is that of a mean deviation of the values of two observables measured jointly, and thus its applicability is limited to cases where such joint measurements are available. The second error measure quantifies the differences between two probability distributions obtained in separate runs of measurements and is of unrestricted applicability. We show that there are no nontrivial unconditional joint-measurement bounds for state-dependent errors in the conceptual framework discussed here, while Heisenberg-type measurement uncertainty relations for state-independent errors have been proven.
In quantum theory, measuring process is an important physical process; it is a quantum description of the interaction between the system of interest and the measuring device. Error and disturbance are used to quantitatively check the performance of the measurement, and are defined by using measuring process. Uncertainty relations are a general term for relations that provide constraints on them, and actively studied. However, the true error-disturbance bound for position measurements is not known yet. Here we concretely construct linear position measurements with minimum error-disturbance in each minimum uncertainty state. We focus on an error-disturbance relation (EDR), called the Branciard-Ozawa EDR, for position measurements. It is based on a quantum root-mean-square (q-rms) error and a q-rms disturbance. We show the theorem that gives a necessary and sufficient condition for a linear position measurement to achieve its lower bound in a minimum uncertainty state, and explicitly give exactly solvable linear position measurements achieving its lower bound in the state. We then give probability distributions and states after the measurement when using them. It is expected to construct measurements with minimum error-disturbance in a broader class of states in the future, which will lead to a new understanding of quantum limits, including uncertainty relations.
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It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a 'weak-measurement', this disturbance can be reduced. One might expect this comes at the cost of also reducing the measurement's precision. However, it was recently demonstrated that a sequence consisting of a weak position measurement followed by a regular momentum measurement can probe a quantum system at a single point, with zero width, in position-momentum space. Here, we study this 'joint weak-measurement' and reconcile its compatibility with the uncertainty principle. While a single trial probes the system with a resolution that can saturate Heisenberg's limit, we show that averaging over many trials can be used to surpass this limit. The weak-measurement does not trade away precision, but rather another type of uncertainty called 'predictability' which quantifies the certainty of retrodicting the measurement's outcome.