Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2203.09921 · Physical Review A

Minimization of the estimation error for entanglement distribution networks with arbitrary noise

Liangzhong Ruan

Published Aug 23, 2023• 7 citations
arXivHTMLPDF

Abstract

Fidelity estimation is essential for the quality control of entanglement distribution networks. Because measurements collapse quantum states, we consider a setup in which nodes randomly sample a subset of the entangled qubit pairs to measure and then estimate the average fidelity of the unsampled pairs conditioned on the measurement outcome. The proposed estimation protocol achieves the lowest mean-square estimation error in a difficult scenario with arbitrary noise and no prior information. Moreover, this protocol is implementation friendly because it only performs local Pauli operators according to a predefined sequence. Numerical studies show that compared to existing fidelity estimation protocols, the proposed protocol reduces the estimation error in both scenarios with independent and identically distributed noise and correlated noise.

DOI
10.1103/physreva.108.022418

Related papers

Error minimization for fidelity estimation of GHZ states with arbitrary noise

Liangzhong Ruan

Fidelity estimation is a crucial component for the quality control of entanglement distribution networks. This work studies a scenario in which multiple nodes share noisy Greenberger-Horne-Zeilinger (GHZ) states. Due to the collapsing nature of quantum measurements, the nodes randomly sample a subset of noisy GHZ states for measurement and then estimate the average fidelity of the unsampled states conditioned on the measurement outcome. By developing a fidelity-preserving diagonalization operation, analyzing the Bloch representation of GHZ states, and maximizing the Fisher information, the proposed estimation protocol achieves the minimum mean squared estimation error in a challenging scenario characterized by arbitrary noise and the absence of prior information. Additionally, this protocol is implementation-friendly as it only uses local Pauli operators according to a predefined sequence. Numerical studies demonstrate that, compared to existing fidelity estimation protocols, the proposed protocol reduces estimation errors in both scenarios involving independent and identically distributed (i.i.d.) noise and correlated noise.

arXiv:2408.09413•Aug 18, 2024•0 citations

Reliable Interval Estimation for the Fidelity of Entangled States in Scenarios with General Noise

Liangzhong Ruan, Bas Dirkse

Fidelity estimation for entangled states constitutes an essential building block for quality control and error detection in quantum networks. Nonetheless, quantum networks often encounter heterogeneous and correlated noise, leading to excessive uncertainty in the estimated fidelity. In this paper, the uncertainty associated with the estimated fidelity under conditions of general noise is constrained by jointly employing random sampling, a thought experiment, and Bayesian inference, resulting in a credible interval for fidelity that is valid in the presence of general noise. The proposed credible interval incorporates all even moments of the posterior distribution to enhance estimation accuracy. Factors influencing the estimation accuracy are identified and analyzed. Specifically, the issue of excessive measurements is addressed, emphasizing the necessity of properly determining the measurement ratio for fidelity estimation under general noise conditions.

arXiv:2409.19282•Sep 28, 2024•0 citations

Optimizing resource bounds in direct fidelity estimation

Netanel Barel, Lee Peleg, Yotam Kadish +2 more

Direct fidelity estimation provides a way to estimate the fidelity between an experimentally prepared state and a desired pure target state without performing full tomography. Two influential formulations were introduced in 2011 by Flammia and Liu and by da Silva, Landon-Cardinal, and Poulin. In these protocols, the total estimation error is controlled through two distinct probabilistic steps: first, the fidelity is approximated using randomly sampled Pauli observables; second, each sampled expectation value is estimated from finitely many measurement outcomes. In this work we show that additional structural information about the noise can substantially sharpen the corresponding resource bounds. In particular, for some canonical channels the effective number of sampled Pauli settings can be reduced, leading to lower measurement cost both in the general pure-state setting and in the case of a stabilizer state. These results illustrate a broader point: worst-case confidence bounds in direct fidelity estimation can be significantly conservative when experimentally relevant structure is ignored. As a technical ingredient, we also revisit the allocation of the total accuracy and confidence budgets between the two probabilistic steps. Reformulating the analysis in terms of separate error parameters yields a constrained optimization problem whose solution lowers the average number of measurements in the general pure-state setting. Numerical simulations based on quantum circuits implemented in Qiskit illustrate both the improvement obtained under structured-noise assumptions and the conservativeness of the original worst-case bounds.

quant-pharXiv:2606.16336•Jun 16, 2026•0 citations

On the fidelity estimation for Entanglement Distribution Protocols

Leonardo A. Gonzalez Z., Riccardo Bassoli, Frank H. P. Fitzek

The distribution of entangled qubits over a noisy quantum channel and its evaluation with a quality metric as the fidelity is a key enabler of future quantum internet. We use a noisy entanglement pair generator providing pairs with dynamic fidelity. Furthermore, we model and implement the quantum channel as a rotational gate which negatively affects the distributed pair’s fidelity over time. Thus, forcing favourable and non-favourable times for the distribution of entanglement in terms of its fidelity. In this dynamic context, the entangled qubits are sequentially generated and distributed, revealing a frame with a certain number of distributed entangled pairs. A frame’s associated fidelity is fundamental to assessing the quality of the distributed pairs. It is computed by measuring a subset of the frame’s entangled pairs; therefore implying an overhead and leaving an effective payload of distributed entangled pairs. Additionally, the accuracy of the estimated frame’s fidelity depends on the amount of measured entangled pairs implying a trade-off between overhead and accuracy. In this work, we analyze the distribution of entanglement for the proposed dynamics by estimating the associated fidelity of frames with varying lengths at different operational points.

IEEE Future Networks World Forum (FNWF)•Oct 15, 2024•0 citations

Sampling Groups of Pauli Operators to Enhance Direct Fidelity Estimation

Júlia Barberà-Rodríguez, Mariana Navarro, Leonardo Zambrano

Direct fidelity estimation is a protocol that estimates the fidelity between an experimental quantum state and a target pure state. By measuring the expectation values of Pauli operators selected through importance sampling, the method is exponentially faster than full quantum state tomography. We propose an enhanced direct fidelity estimation protocol that uses fewer copies of the experimental state by grouping Pauli operators before the sampling process. We derive analytical bounds on the measurement cost and estimator variance, showing improvements over the standard method. Numerical simulations validate our approach, demonstrating that for 8-qubit Haar-random states, our method achieves a one-third reduction in the required number of copies and reduces variance by an order of magnitude using only local measurements. These results underscore the potential of our protocol to enhance the efficiency of fidelity estimation in current quantum devices.

arXiv:2501.19228•Quantum•Jul 3, 2025•3 citations

Fidelity Estimation of Entangled Measurements with Local States

Zanqiu Shen, Kun Wang

We propose an efficient protocol to estimate the fidelity of an $n$-qubit entangled measurement device, requiring only qubit state preparations and classical data post-processing. It works by measuring the eigenstates of Pauli operators, which are strategically selected according to their importance weights and collectively contributed by all measurement operators. We rigorously analyze the protocol's performance and demonstrate that its sample complexity is uniquely determined by the number of Pauli operators possessing non-zero expectation values with respect to the target measurement. Moreover, from a resource-theoretic perspective, we introduce the stabilizer Rényi entropy of quantum measurements as a precise metric to quantify the inherent difficulty of estimating measurement fidelity.

arXiv:2312.13730•Dec 21, 2023•0 citations
Fidelity estimation is essential for the quality control of entanglement distribution networks. Because measurements collapse quantum states, we consider a setup in which nodes randomly sample a subset of the entangled qubit pairs to measure and then estimate the average fidelity of the unsampled pairs conditioned on the measurement outcome. The proposed estimation protocol achieves the lowest mean-square estimation error in a difficult scenario with arbitrary noise and no prior information. Moreover, this protocol is implementation friendly because it only performs local Pauli operators according to a predefined sequence. Numerical studies show that compared to existing fidelity estimation protocols, the proposed protocol reduces the estimation error in both scenarios with independent and identically distributed noise and correlated noise.
Fidelity estimation is a crucial component for the quality control of entanglement distribution networks. This work studies a scenario in which multiple nodes share noisy Greenberger-Horne-Zeilinger (GHZ) states. Due to the collapsing nature of quantum measurements, the nodes randomly sample a subset of noisy GHZ states for measurement and then estimate the average fidelity of the unsampled states conditioned on the measurement outcome. By developing a fidelity-preserving diagonalization operation, analyzing the Bloch representation of GHZ states, and maximizing the Fisher information, the proposed estimation protocol achieves the minimum mean squared estimation error in a challenging scenario characterized by arbitrary noise and the absence of prior information. Additionally, this protocol is implementation-friendly as it only uses local Pauli operators according to a predefined sequence. Numerical studies demonstrate that, compared to existing fidelity estimation protocols, the proposed protocol reduces estimation errors in both scenarios involving independent and identically distributed (i.i.d.) noise and correlated noise.
Fidelity estimation for entangled states constitutes an essential building block for quality control and error detection in quantum networks. Nonetheless, quantum networks often encounter heterogeneous and correlated noise, leading to excessive uncertainty in the estimated fidelity. In this paper, the uncertainty associated with the estimated fidelity under conditions of general noise is constrained by jointly employing random sampling, a thought experiment, and Bayesian inference, resulting in a credible interval for fidelity that is valid in the presence of general noise. The proposed credible interval incorporates all even moments of the posterior distribution to enhance estimation accuracy. Factors influencing the estimation accuracy are identified and analyzed. Specifically, the issue of excessive measurements is addressed, emphasizing the necessity of properly determining the measurement ratio for fidelity estimation under general noise conditions.
Direct fidelity estimation provides a way to estimate the fidelity between an experimentally prepared state and a desired pure target state without performing full tomography. Two influential formulations were introduced in 2011 by Flammia and Liu and by da Silva, Landon-Cardinal, and Poulin. In these protocols, the total estimation error is controlled through two distinct probabilistic steps: first, the fidelity is approximated using randomly sampled Pauli observables; second, each sampled expectation value is estimated from finitely many measurement outcomes. In this work we show that additional structural information about the noise can substantially sharpen the corresponding resource bounds. In particular, for some canonical channels the effective number of sampled Pauli settings can be reduced, leading to lower measurement cost both in the general pure-state setting and in the case of a stabilizer state. These results illustrate a broader point: worst-case confidence bounds in direct fidelity estimation can be significantly conservative when experimentally relevant structure is ignored. As a technical ingredient, we also revisit the allocation of the total accuracy and confidence budgets between the two probabilistic steps. Reformulating the analysis in terms of separate error parameters yields a constrained optimization problem whose solution lowers the average number of measurements in the general pure-state setting. Numerical simulations based on quantum circuits implemented in Qiskit illustrate both the improvement obtained under structured-noise assumptions and the conservativeness of the original worst-case bounds.
The distribution of entangled qubits over a noisy quantum channel and its evaluation with a quality metric as the fidelity is a key enabler of future quantum internet. We use a noisy entanglement pair generator providing pairs with dynamic fidelity. Furthermore, we model and implement the quantum channel as a rotational gate which negatively affects the distributed pair’s fidelity over time. Thus, forcing favourable and non-favourable times for the distribution of entanglement in terms of its fidelity. In this dynamic context, the entangled qubits are sequentially generated and distributed, revealing a frame with a certain number of distributed entangled pairs. A frame’s associated fidelity is fundamental to assessing the quality of the distributed pairs. It is computed by measuring a subset of the frame’s entangled pairs; therefore implying an overhead and leaving an effective payload of distributed entangled pairs. Additionally, the accuracy of the estimated frame’s fidelity depends on the amount of measured entangled pairs implying a trade-off between overhead and accuracy. In this work, we analyze the distribution of entanglement for the proposed dynamics by estimating the associated fidelity of frames with varying lengths at different operational points.
Direct fidelity estimation is a protocol that estimates the fidelity between an experimental quantum state and a target pure state. By measuring the expectation values of Pauli operators selected through importance sampling, the method is exponentially faster than full quantum state tomography. We propose an enhanced direct fidelity estimation protocol that uses fewer copies of the experimental state by grouping Pauli operators before the sampling process. We derive analytical bounds on the measurement cost and estimator variance, showing improvements over the standard method. Numerical simulations validate our approach, demonstrating that for 8-qubit Haar-random states, our method achieves a one-third reduction in the required number of copies and reduces variance by an order of magnitude using only local measurements. These results underscore the potential of our protocol to enhance the efficiency of fidelity estimation in current quantum devices.
We propose an efficient protocol to estimate the fidelity of an nnn-qubit entangled measurement device, requiring only qubit state preparations and classical data post-processing. It works by measuring the eigenstates of Pauli operators, which are strategically selected according to their importance weights and collectively contributed by all measurement operators. We rigorously analyze the protocol's performance and demonstrate that its sample complexity is uniquely determined by the number of Pauli operators possessing non-zero expectation values with respect to the target measurement. Moreover, from a resource-theoretic perspective, we introduce the stabilizer Rényi entropy of quantum measurements as a precise metric to quantify the inherent difficulty of estimating measurement fidelity.