Researchers from the University of Science and Technology of China, including Suxia Yu, Liangliang Sun, Xiang Zhou, along with Zhenpeng Xu from Anhui University and Armin Tavakoli from Lund University, have collaborated to discover that experimental data originally used only for detecting the presence of entanglement can now be utilized to estimate its size. The team leverages the average value of commonly used entangled witnesses to provide estimates for lower bounds on almost all commonly used entanglement measures under three typical experimental conditions, effectively transforming entanglement detection experiments into experiments for estimating entanglement size at zero additional cost. The relevant findings have recently been published in Physical Review Letters.
Quantum entanglement, a fundamental concept in quantum theory and a core resource in quantum information, entails two primary tasks in research: entanglement detection and measurement. In experiments, effective detection and estimation of entanglement size are prerequisites for accomplishing various information tasks, especially estimating the size of entanglement, which determines the efficiency of utilizing this valuable resource.
Entangled witnesses, simply put, are observables. When their average value falls below a certain threshold, it indicates the presence of system entanglement. Any given entangled state can be detected by an appropriate entangled witness. Due to their simplicity and strong detection capabilities, entangled witnesses have become the preferred tools for detecting entanglement in experiments, applicable in various experimental scenarios such as trustworthy devices, untrustworthy measurement apparatus, and completely untrustworthy experimental setups. However, until now, all entangled witnesses have typically been used solely for detecting the presence or absence of entanglement, remaining silent on the estimation of entanglement size.
The research team discovered that entangled witnesses can be appropriately normalized into a form of distance, which characterizes the distinguishability between experimental data generated by a given quantum state and separable states under the same measurement. This distinguishability lies at the core of quantifying entanglement and can be linked to various common entanglement measures. Under conditions where the devices are entirely trustworthy, the normalized entangled witness describes the optimal distinguishability between a given state and separable states, while under conditions where the experimental setup is entirely untrustworthy, it describes the optimal distinguishability between the quantum correlations generated by a given state and the local correlations generated by separable states. A similar normalization can also be applied under conditions where the measurement apparatus is untrustworthy.
Ultimately, regardless of the experimental conditions under which entangled witnesses are employed, as long as entanglement can be detected, experimenters can calculate lower bounds on various entanglement measures based on the average value of the entangled witness, rendering entangled witnesses no longer silent. For multipartite systems, normalized entangled witnesses can also be used to estimate the depth of entanglement, indicating how many particles in the system are entangled together. Under the asymptotic condition of an infinite number of particles, this method rigorously provides lower bounds on entanglement measures based on trace distance for certain systems, thereby yielding accurate estimates of entanglement size.
Reviewers highly praised the method proposed by this team, stating that it "comprehensively addresses an important issue, extending entanglement experiments to numerous entanglement measures."
For more information, please refer to the related paper: Physical Review Letters - Research Article
