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arXiv:2208.01083 · Advanced Quantum Technologies

Efficient Verification of Arbitrary Entangled States with Homogeneous Local Measurements

Ye‐Chao Liu, Yinfei Li, Jiangwei Shang, Xiangdong Zhang

Published Jun 13, 2023• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/qute.202300083

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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.
Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterize the output state by quantum state tomography, or alternatively, to perform some kind of Bell test, tailored to the state of interest. We show here that neither approach is optimal among local verification strategies for 2-qubit states. We find the optimal strategy in this case and show that quadratically fewer total measurements are needed to verify to within a given fidelity than in published results for quantum state tomography, Bell test, or fidelity estimation protocols. We also give efficient verification protocols for any stabilizer state. Additionally, we show that requiring that the strategy be constructed from local, nonadaptive, and noncollective measurements only incurs a constant-factor penalty over a strategy without these restrictions.
Efficient and reliable verification of quantum states is central to quantum information processing applications. If using well-characterized measurement devices, effective methods have been developed for quantum state verification (QSV). In reality, however, measurement devices are generally imperfect or untrusted, which limits significantly the application of standard QSV protocols. Here, we propose the measurement-device-independent QSV (MDI-QSV) scheme for practice. With the help of trusted quantum inputs, we have developed a systematical approach to design MDI-QSV strategies for an arbitrary pure target state. We find that the number of required measurements has an optimal scaling with required accuracy and confidence level, similar to the standard QSV where trusted measurement devices are available. Our results offer a sample-efficient and realistic method for quantum state verification with virtues of a measurement-device-independent manner, and are within reach of current technology.
We develop a framework for quantum measurement verification (QMV) using only local state preparations. For locally transitive and irreducible projective measurements, we prove that symmetry reduces locality constrained QMV to quantum state verification of a single basis state, thereby reducing protocol design to the optimization of homogeneous verification operators. We apply the framework to generalized Bell measurements, single-parameter measurements on two qubits, elegant joint measurements, and stabilizer state induced measurements, and derive explicit local protocols together with closed form verification operators, success probabilities, and sample complexities. We further show that homogeneous QMV protocols can estimate measurement fidelity directly from observed passing frequencies.
The efficient and reliable characterization of quantum states plays a vital role in most, if not all, quantum information processing tasks. In this work, we present a universally optimal protocol for verifying entangled states by employing the so-called quantum nondemolition measurements, such that the verification efficiency is equivalent to that of the optimal global strategy. Instead of being probabilistic as the standard verification strategies, our protocol is constructed sequentially, which is thus more favorable for experimental realizations. In addition, the target states are preserved in the protocol after each measurement, so can be reused in any subsequent tasks. We demonstrate the power of our protocol for the optimal verification of Bell states, arbitrary two-qubit pure states, and stabilizer states. We also prove that our protocol is able to perform tasks including fidelity estimation and state preparation.
Abstract The quantum verification is to determine whether a quantum device is intentionally deceptive by assessing the proximity between the actual output state and the expected state. As a crucial step toward the advancement of quantum technology, numerous quantum state verification methods have been proposed. However, there remains a scarcity of methods for verifying states with an arbitrary number of qubits. A verification strategy for the entangled states with is proposed. Specifically, an average map is introduced and demonstrated that it simplifies the matrix form of the verification strategy while maintaining the verification efficiency. By optimizing the verification strategies, the strategy with local projective measurements is obtained.
Efficient verification of entangled states is crucial to many applications in quantum information processing. However, the effectiveness of standard quantum state verification (QSV) is based on the condition of independent and identical distribution (IID), which impedes its applications in many practical scenarios. Here we demonstrate a defensive QSV protocol, which is effective in all kinds of non-IID scenarios, including the extremely challenging adversarial scenario. To this end, we build a high-speed preparation-and-measurement apparatus controlled by quantum random-number generators. Our experiments clearly show that standard QSV protocols often provide unreliable fidelity certificates in non-IID scenarios. In sharp contrast, the defensive QSV protocol based on a homogeneous strategy can provide reliable and nearly tight fidelity certificates at comparable high efficiency, even under malicious attacks. Moreover, our scheme is tolerant of the imperfections in a realistic experiment, which is very appealing to practical applications.