Entanglement
Entanglement is a quantum mechanical phenomenon in which the states of two or more qubits are linked together in such a way that they cannot be described independently. This means that the measurement of one qubit can affect the state of the other qubits.
How Entanglement Works
An entangled state is characterized by its inability to be represented as a tensor product of individual states. This means that the state of two qubits cannot be written as the product of the states of the individual qubits.
For example, the state |00⟩ can be written as the tensor product of the states |0⟩ and |0⟩:
|00⟩ = |0⟩ ⊗ |0⟩
However, the entangled state 1/√2(|00⟩ + |11⟩) cannot be written as the tensor product of two individual states. This is because the state of the two qubits is not simply the product of the states of the individual qubits.
The Correlation Between Entanglement States
The state 1/√2(|00⟩ + |11⟩) shows that the states of the two qubits are correlated. This means that if the state of one qubit is |1⟩, then the state of the other qubit is also |1⟩. Similarly, if the state of one qubit is |0⟩, then the state of the other qubit is also |0⟩.
This correlation between the states of the two qubits is a key feature of entanglement. It is this correlation that allows entangled states to be used for quantum computing tasks, such as Shor's algorithm for factoring large numbers.
How Do We Create Entanglement?
Entanglement can be created using a variety of quantum gates. One common way to create entanglement is to use the Hadamard gate and the controlled-NOT gate.
The combination of the Hadamard and CNOT gates acts on the state |00⟩ as follows:
This shows that the Hadamard and CNOT gates can be used to create an entangled state.
Applications of Entanglement
Entanglement has a wide range of potential applications in quantum computing. For example, entangled states can be used to perform quantum teleportation, which allows for the transfer of quantum information between two distant locations. Entanglement can also be used to perform quantum cryptography, which allows for secure communication between two parties.
Entanglement is a powerful quantum phenomenon with the potential to revolutionize the way we compute and communicate. As research in quantum computing continues, we can expect to see even more applications for entanglement in the years to come.