Amplitude-amplified Coherence Detection Achieves State Estimation with Reduced Sample Complexity
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Detecting and quantifying coherence is crucial for advancing both fundamental quantum theory and emerging quantum technologies, where coherence directly links to potential advantages. Rhea Alexander, Michalis Skotiniotis, and Daniel Manzano, all from Universidad de Granada, present a new approach to this challenge, developing protocols capable of identifying coherence in previously unknown quantum states. Their work overcomes limitations of existing methods, which can only detect coherence in specific states, and significantly reduces the number of samples needed for accurate detection. By combining a technique called amplitude amplification with phase estimation, the researchers not only detect coherence more efficiently, but also estimate its magnitude with improved precision, offering a new way to interpret and measure this essential quantum property and establishing clear limits on the amount of noise these protocols can withstand. Quantum Coherence and State Distinguishability This research delves into the fundamental aspects of quantum information theory, specifically focusing on quantum coherence and the ability to distinguish between different quantum states or operations, while also considering the computational resources required for these tasks. Scientists explore how efficiently we can determine the properties of quantum systems, laying the groundwork for advancements in quantum technologies.,.
Detecting Coherence With Minimal State Copies Scientists have developed innovative protocols for detecting and quantifying coherence in unknown quantum states, addressing a critical challenge in advancing quantum technologies. The study focused on determining the minimum number of state copies or unitary transformations needed to verify coherence, establishing a direct link to the geometric measure of coherence. Researchers demonstrated that detecting coherence requires a number of state copies that scales inversely with the geometric measure of coherence, a key indicator of the state’s quantum properties. This establishes a fundamental limit on the resources needed for this essential quantum characterization. To significantly reduce experimental demands, the team devised a protocol leveraging access to the unitary transformation that prepares the unknown state. This allowed them to employ amplitude amplification, a technique originally developed for quantum algorithms, to achieve a quadratically smaller sample complexity. By combining amplitude amplification with amplitude estimation, scientists obtained experimental estimations of upper bounds on the geometric measure of coherence with improved precision, offering a substantial improvement over standard estimation methods. This work establishes a new interpretation for the geometric measure of coherence, directly connecting it to the average number of samples needed in the amplitude estimation protocol. Researchers also derived bounds on the amount of noise these protocols can tolerate, further enhancing their practical applicability and paving the way for more efficient verification of quantum systems.,.
Minimum Measurements Reliably Detect Quantum Coherence Scientists have achieved a breakthrough in detecting coherence in quantum states, a fundamental property crucial for advancing quantum technologies. This work establishes the minimum number of measurements needed to reliably determine if an unknown quantum state possesses coherence, a key characteristic linked to potential advantages in computation and communication.
The team developed protocols that significantly reduce the experimental resources required for this task, paving the way for more efficient quantum devices. Researchers demonstrated that detecting coherence in an unknown pure state requires a number of copies of the state that scales inversely with the geometric measure of coherence. This establishes a fundamental limit on the resources needed for this essential quantum characterization. Furthermore, the team devised a protocol that leverages amplitude amplification, a technique inspired by Grover’s algorithm, to further reduce the required number of samples. By augmenting amplitude amplification with phase estimation, they achieved an experimental estimation of upper bounds on the geometric measure of coherence with a sample complexity that scales more efficiently than traditional methods. This represents a substantial improvement in efficiency, allowing for more precise and rapid determination of coherence. The average number of samples needed in this amplitude estimation protocol provides a new interpretation for the geometric measure of coherence, linking a theoretical quantity to a practical measurement. Finally, the researchers investigated the robustness of their protocols to noise, demonstrating the limits of tolerance and providing guidelines for practical implementation.,.
Efficient Coherence Detection and Quantification This research presents new protocols for detecting and quantifying coherence in unknown quantum states.
Scientists have established that any method for reliably detecting coherence requires a certain number of measurements, specifically scaling with the geometric measure of coherence of the system. However, by leveraging techniques similar to those used in quantum algorithms, the team developed a protocol that significantly reduces the number of measurements needed, achieving a substantial improvement in efficiency. Furthermore, the researchers demonstrated a method for estimating bounds on the geometric measure of coherence with enhanced precision, requiring fewer samples than traditional Monte Carlo approaches. This advancement provides a new interpretation for the geometric measure of coherence, linking it directly to the average number of measurements needed in their estimation protocol.
The team also investigated the robustness of these protocols, determining the levels of noise they can tolerate while still accurately detecting and quantifying coherence. The researchers anticipate that these protocols will be particularly valuable as quantum computing technology advances and fault-tolerant quantum systems become more readily available. 👉 More information 🗞 Amplitude-amplified coherence detection and estimation 🧠 ArXiv: https://arxiv.org/abs/2512.15352 Tags: