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What is Quantum entanglement?

A link between the states of several qubits that cannot be written as a combination of the states of the individual qubits. In (|00⟩ + |11⟩)/√2, the two measurement results always agree. It is one of the sources of the computing power of quantum computers, but it cannot be used to send information faster than light.

Japanese name: 量子もつれ

Quantum entanglement appears in 2 practice questions across 1 topic, including Quantum Computing Hardware.

Field: Quantum Computing Hardware

Try it: questions about Quantum entanglement

Two qubits are in the entangled state (|00⟩ + |11⟩)/√2. Which statement is correct?

  1. AEven when the first qubit is measured, the second qubit stays in a state giving 0 and 1 with 50% probability each
  2. BIf measuring the first qubit gives 0, the second is certain to be 0, and if it gives 1, the second is certain to be 1
  3. CBy choosing the measurement result of the first qubit, information can be sent faster than light to the second qubit far away
Show answer and explanation

Answer: B. If measuring the first qubit gives 0, the second is certain to be 0, and if it gives 1, the second is certain to be 1

This state is a superposition of |00⟩ and |11⟩ with no |01⟩ or |10⟩ component, so the two measurement results always agree. Looking at either qubit alone, 0 and 1 each appear 50% of the time, but the results are correlated in a way that two independent bits cannot explain; this is quantum entanglement. However, which result appears is random and cannot be chosen by the person measuring, so entanglement cannot be used to send information faster than light. In a quantum computer, the quality of the two-qubit gates that create entanglement strongly affects performance.

Starting from the two-qubit state |00⟩ (the left digit is the first qubit), an H gate is applied to the first qubit, followed by a CNOT gate with the first qubit as control and the second as target. What is the resulting state?

  1. A(|00⟩ + |11⟩)/√2
  2. B(|00⟩ + |10⟩)/√2
  3. C(|01⟩ + |10⟩)/√2
Show answer and explanation

Answer: A. (|00⟩ + |11⟩)/√2

The H gate puts the first qubit into superposition, giving (|00⟩ + |10⟩)/√2. The CNOT gate flips the target only when the control is 1, so |10⟩ becomes |11⟩ and the state becomes (|00⟩ + |11⟩)/√2. This is an entangled state called a Bell state, in which the measurement results of the two qubits always agree. The combination of an H gate and a CNOT gate is the most basic circuit for creating entanglement.

Quantum entanglement in the explanations

Questions that mention Quantum entanglement (2)

  1. Two qubits are in the entangled state (|00⟩ + |11⟩)/√2. Which statement is correct?
  2. Starting from the two-qubit state |00⟩ (the left digit is the first qubit), an H gate is applied to the first qubit, followed by a CNOT gate with the first qubit as control and the second as target. What is the resulting state?

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Related terms

Qubit Quantum superposition Decoherence Dilution refrigerator Ion trap Josephson junction NISQ Post-quantum cryptography Quantum error correction Quantum gate

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