Recently, scientists tested whether quantum correlation exists at energies never explored so far (~13TeV). They used top-quark pairs at the Large Hadron Collider (LHC), the world’s largest and most powerful particle accelerator. Their result showed an affirmative result of the existing quantum correlation. In the following articles, I will briefly discuss what is quantum correlation and how to show its existence with Bell Inequality.
Quantum Correlation (Quantum Entanglement)
The distinct feature in distinguishing classical and quantum physics is quantum correlation, also known as quantum entanglement. Let’s use an example to explain quantum correlation. This example is called the daily surprise package. Imagine that you and your friend, Tim, both get a daily package from a Quantum company. Quantum company creates the quantum correlation between your and Tim’s package. When opening the package, you only see either a blue or red balloon. Today, you get a red balloon. Quantum theory enables you to predict what color Tim gets with 100% precision regardless of the distance between you and Tim.
Why do we need Quantum theory? Maybe a classical lottery machine is enough.
This mysterious nonlocal property confused people, even the greatest scientists, such as Albert Einstein. To avoid accepting this strange concept of quantum correlation, Einstein instead developed a classical theory, the hidden-variables theory, and claimed this should be the underlying theory of Quantum theory. How do we understand this hidden variable in the daily surprise package example? This idea is that Quantum company actually uses lottery machines to randomly put the balloons in the package. Einstein stated that the random lottery machine exists behind quantum theory. Classical theory is enough to understand quantum correlations.
Bell Inequality
However, in 1964, John Bell showed classical hidden variables theory and Quantum theory are incompatible. He also introduced Bell Inequality to quantitatively distinguish classical and quantum correlations. In Bell Inequality, he derived a upper bound for the classical correlation from the hidden-variables theory. As for quantum theory, the resultant quantum correlation can exceed this bound. Therefore, the violation of Bell Inequality indicates the existence of quantum correlation.
Loopholes in testing Bell Inequality in real experiments
In theory side, classical hidden-variabes theory and Quantum theory result in different correlation properties between particles. How do we experimentally determine whether our system is more classical or quantum ? In principle, we have to measure these particles independently for multiple times. Based on the measurement results, we compute the correlation and test whether the Bell Inequality is satisfied. However, these procedures have several loopholes in real experiment setup. One typical loophole is the detection loophole which comes from the inefficiency in detectors. Sometimes the detector might not read the output of the measurement. These flawed data strongly affect the correlation and the Bell Inequality test. Similar loopholes also happen due to how we measure these particles. Thus, testing the Bell Inequality in real experiment requires careful experiment design and data analysis.