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arXiv:2410.00554 · Physical Review A

Beating the optimal verification of entangled states via collective strategies

Ye‐Chao Liu, Jiangwei Shang

Published Nov 10, 2025• 0 citations
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Abstract

This work presents a collective strategy for verifying entangled quantum states that can reach efficiencies beyond those obtainable with the standard global-measurement approach, while preserving unused copies. The protocol is scalable across various platforms and is able to provide information about noise in the system.
DOI
10.1103/6yrh-9tzp

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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.
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, reliable characterization of quantum states is a basic and important step in most tasks in quantum information processing, but standard approaches, including quantum tomography, are notoriously inefficient. This research offers solutions to the problem of verifying nonstabilizer states by proposing efficient, practical protocols for verifying arbitrary nnn-qubit Dicke states. These protocols require only two distinct settings based on Pauli measurements, and thus are readily applicable with current experimental techniques, and are able to verify the robust Dicke states of hundreds of qubits.
Verifiable blind quantum computation provides a cloud scenario for scalable quantum information processing. However, constructing one resource-efficient verification protocol is still an open problem. In this paper, the context of verification we consider is the measurement-based model, in which the client receives the graph state prepared by the server and performs single-qubit measurements on it to drive the computation. We first utilize three entanglement witnesses to estimate the fidelity of the prepared graph state. Applying entanglement witnesses to design the test phase, we propose verification protocols. Our protocol requires overhead in terms of copies of the graph state that scales as O(n2logn)O({n}^{2}logn)O(n2logn), where nnn is the number of qubits of the graph state. Furthermore, the soundness of our protocol is improved. The advantages of our protocol are derived from the fact that each entanglement witness can be implemented by the client with a fixed number of measurement settings.
Graph and hypergraph states are of wide interest in quantum information processing as well as fundamental physics, and efficient verification of these states is key to various applications. The authors propose a simple recipe for verifying hypergraph states that requires only two distinct Pauli measurements for each party, and is dramatically more efficient than conventional protocols based on local measurements. This approach enables verification of hypergraph states and genuine multipartite entanglement of thousands of qubits, even in an adversarial scenario.