Entanglement: linked qubits

Entangle two qubits with a CNOT gate: random on their own but always in agreement together. The phenomenon Einstein called “spooky action at a distance”.

CNOT: controlled NOT

So far we have applied gates to single qubits. CNOT works on two qubits: if the control qubit is 1 it flips the target qubit (applies X), if it is 0 it does nothing. It is like a classical “if” statement.

In the playground, for two-qubit gates you click the + button of the control qubit first, then of the target. In the circuit the control appears as a dot (●) and the target as a circle with a plus (⊕).

The Bell state

Apply H to the first qubit, then link it to the second with a CNOT. Because the first qubit is in superposition, the CNOT is in a “flip and don’t flip” state. The two qubits end up in a single joint state: 00 or 11, half of the time each. This is called a Bell state.

Measure 1000 times: 00 and 11 come out about equally often, but 01 or 10 never appear even once. Each qubit on its own is completely random, yet the two always give the same result. This link is called entanglement.

Spooky action at a distance

Even if you take two entangled qubits kilometres apart, the agreement remains. Einstein could not accept this and called it “spooky action at a distance”. Perhaps the results had been secretly fixed from the start?

In 1964 John Bell showed that this question could be tested experimentally. The experiments of Alain Aspect, John Clauser and Anton Zeilinger proved that entanglement cannot be explained by hidden predetermination, earning them the 2022 Nobel Prize in Physics.

An important note: entanglement does not allow sending messages faster than light. Each side sees only random results on its own; the agreement shows up only when the results are compared over an ordinary channel.

What is entanglement good for?

Entanglement is an indispensable resource of quantum computing: circuits without entanglement can easily be simulated by classical computers. It is also the foundation of applications such as quantum teleportation, quantum cryptography and quantum error correction.

Try it yourself

Measure the Bell state 1000 times: 01 and 10 never appear. Then click the CNOT in the circuit to remove it and measure again: with no entanglement the second qubit is always 0 and only 00 and 01 appear. Finally, look at the three-qubit GHZ example.

Open the circuit in your browser

The circuit playground is in Turkish. Button guide: “1000 kez ölç” = measure 1000 times, “Durum vektörünü göster” = show the state vector, “Bu devrenin Qiskit kodu” = this circuit’s Qiskit code, “Geri al” = undo, “Temizle” = clear. Click a gate in the circuit to remove it.

Key points

CNOT flips the target qubit if the control qubit is 1.
H followed by CNOT puts two qubits into an entangled Bell state: the result is 00 or 11.
Entangled qubits are random one by one but always agree together.
Entanglement gives no faster-than-light communication, but it is a key resource for quantum computing and communication.

Test yourself

You measured the first of two qubits in a Bell state and saw 1. What does the second qubit give?

Certainly 1
Certainly 0
1 with 50% probability

Show the answer

Certainly 1. In the Bell state only 00 and 11 are possible. If the first qubit gave 1, the second is certainly 1 as well.

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