Entanglement is a many-body property in [[quantum mechanics]]. In order to observe entanglement, we need at least two quantum systems. It describes a form of correlation between two particles that is stronger than any classical form of correlation. As a concrete example, we can take the [[Spin|spin]] of two [[Electron|electrons]]. We can visualize the spin as an arrow pointing in one of two direction: either up or down. Of course, it can also be in a [[superposition]] of these two states. If we take two electrons, there are four ways that the spins of the two electrons could point. ![[enuemration_two_spins.excalidraw.light.svg]] We can now choose to only use Option 1 and Option 4 in a superposition. Thus, they spins always point in the same direction, either both up or both down. ![[bell_state_spin.excalidraw.light.svg]] If we measure the first spin and obtain the result up, then we know that the second spin must point up as well. After all, we prepared them such that they always point into the same direction. Interestingly, we never specified that the two spins have to be close to each other. Thus, the spins would still point in the same direction even if they were far apart. Since they are in a superposition of Option 1 and Option 4, upon measurement they will select one of the two configurations (either Option 1 or Option 4). And no matter how far the spins are apart, they will always point in the same direction. This is the power of entanglement If two quantum mechanical systems cannot be described separately, then they are entangled. A typical example is two qubits that always both yield $0$ or $1$ when measured. As soon as one [[Qubit|qubit]] is measured, the state of the second [[Qubit|qubit]] is also determined. >[!read]- Further Reading > - [[Qubit]] >[!ref]- References