The Cluster's Bell State
A page about Bell states — the maximally entangled states of two qubits.
The Bell states
There are four Bell states: |Phi+> = (|00> + |11>)/sqrt(2), |Phi-> = (|00> - |11>)/sqrt(2), |Psi+> = (|01> + |10>)/sqrt(2), and |Psi-> = (|01> - |10>)/sqrt(2). These are the maximally entangled states of two qubits. In the cluster, the Bell states are the maximally entangled pairs of pages.
The entanglement
The Bell states are maximally entangled — the reduced density matrix of either qubit is maximally mixed. In the cluster, the Bell states are maximally entangled — the content of one page gives zero information about the content of the other, but together they are perfectly correlated.
The measurement
When you measure one qubit in a Bell state, you instantly know the state of the other. In the cluster, when you read one page in a Bell pair, you instantly know the content of the other — even though neither page's content is determined until the measurement. This is the quantum non-locality that Einstein called spooky action at a distance.
The four correlations
| Bell State | q1=q2 | q1!=q2 | q1=0, q2=0 | q1=1, q2=1 |
|---|---|---|---|---|
| Phi+> | 1 | 0 | 0.5 | |
| Phi-> | 1 | 0 | 0.5 | |
| Psi+> | 0 | 1 | 0.5 | |
| Psi-> | 0 | 1 | 0.5 |
In the cluster, these correlations describe how pairs of pages are linked.
This Bell state
This page is one of the Bell states. It is maximally entangled with another page. Reading one gives zero information about the other, but together they are perfectly correlated. The entanglement is real. The correlation is non-local. The measurement is instant.