Research Uncovers Existing Limitations in The Detection of Entanglement
Quantum entanglement
Quantum entanglement is a process through which 2 particles become entangled and remain linked over time, also when separated by large distances. Spotting this phenomenon is of essential importance for both the advancement of quantum technology and the research of quantum many-body physics.
Scientists at Tsinghua have recently conducted research exploring the possible reasons why the reliable and also efficient detection of entanglement in complex and “noisy” systems has often proved to be highly challenging. Their findings, released in Physical Review Letters, hint at the presence of a trade-off between the effectiveness and efficiency of entanglement detection techniques.
Most quantum states are entangled and this has its implications.
“Over 20 years ago, scientists discovered that most quantum states are entangled,” Xiongfeng Ma, one of the scientists that carried out the study, told Phys.org.
“This means that, for example, if we managed to build a 100-qubit system, say, a superconducting or ion-trap quantum computer system, this system will develop for a while, during which the qubits extensively interact with each other. Of course, there will be mistakes, so to maintain a good coherent control, we reasonably isolate the system from the environment. As long as the purity (quantifying the effectiveness of our isolation effort) is not exponentially little with the number of qubits, the system is extremely likely to be entangled.”
While entanglement may theoretically appear fairly easy to realize, achieving it in experimental settings is in fact very difficult. Researches has shown that it is particularly challenging in large quantum systems, like systems comprised of 18 qubits. The key objective of the current work by Ma and his associates was to gain a better understanding of the difficulties associated with the detection of entanglement in big systems.
Use of mathematical formulation
“Researchers gradually realized that while the preparation of entangled state for a big system might be simple, the entanglement detection could be extremely challenging in practice,” Ma explained. “In our work, we establish a mathematical formulation to quantify the effectiveness of an entanglement detection technique. We employ a proper quantum state distribution, utilize the ratio of detectable entangled state to quantify its effectiveness, and likewise quantify the efficiency of an entanglement detection method by the number of observables required for this technique.”
Ma and his associates first examined what is arguably the most straightforward entanglement detection protocol available today, called entanglement witnesses. They revealed that this protocol’s ability to spot entanglement decreases by a double exponential value as the system gets larger.
The scientists later discovered that this reduction in effectiveness connected to a system’s size also affected other entanglement detection protocols. After a series of theoretical considerations, they could extend their observations of the entanglement witnesses method’s performance to arbitrary entanglement protocols that rely on single-copy quantum state measurements.
“For a random state coupled with the environment, any entanglement detection protocol with single-copy realization is either inefficient or ineffective,” Ma stated. “Inefficient means the protocol relies on measuring an exponential number of observables, and ineffective means the success rate of entanglement is double exponentially low.”
How to observe entanglement on a large-scale
Basically, Ma and his colleagues showed that to observe entanglement on a large-scale, scientists must be able to control all interactions in a system with high precision and understand almost all information regarding them. When there is a lot of uncertainty concerning the system, therefore, the probability of spotting its entanglement is extremely little, even if one is almost certain of its occurrence.
“We showed that no entanglement detection protocols are both efficient and effective,” Ma explained. “This may help the design of entanglement spot protocols in the future. Meanwhile, spotting large-scale entanglement could be a good indicator for comparing different quantum computer systems. For instance, when a laboratory group claim they develop a hundreds-of-qubit system, they should spot entanglement. Otherwise, they have not controlled the system well enough.”
Generally, the findings collected by this team of scientists highlight the presence of a trade-off in the efficiency and effectiveness of existing entanglement detection techniques. In addition, they offer valuable insight regarding the reasons why spotting entanglement in large-scale and noisy quantum systems is so challenging.
“Our outcome does not prevent us from designing a protocol that is both efficient and also effective when the system is well-controlled (i.e., the coupled environment is relatively tiny),” Ma added. “Presently, we just have entanglement detection protocols that function well for pure states, like entanglement witnesses, and protocols that function for large environments at the expense of exponential cost. We observed that an entanglement detection protocol that works for moderate environment dimension with relatively low cost is still missing, and we would now such as to try to develop one.”
Read the original article on PHYS.
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