Quantum teleportation is a fundamental concept in quantum information theory that allows the transfer of quantum states from one location to another without physically moving the particles themselves. It relies on a phenomenon called entanglement, where two or more particles become correlated in such a way that their states are interconnected.
In quantum teleportation, the sender (Alice) wants to transmit the quantum state of a particle to the receiver (Bob). The process involves the following steps:
Initialization: Alice and Bob share a pair of particles that are entangled. This pair is known as a Bell pair or a maximally entangled state. The Bell pair can be represented as:
|Φ^+⟩ = (1/√2) (|00⟩ + |11⟩),
where |0⟩ and |1⟩ represent two possible quantum states of a single qubit.
Entanglement of the particle to be teleported: Alice takes the particle she wants to teleport (let's call it qubit A) and combines it with her half of the entangled pair (qubit B) through a quantum operation known as a Bell measurement. This measurement entangles qubits A and B further.
Measurement and classical communication: Alice performs a measurement on her two entangled qubits (A and B) and obtains two classical bits as a result. She then communicates these measurement outcomes to Bob through a classical channel, such as a phone call or a computer network.
Conditional operation: Upon receiving the classical information from Alice, Bob applies a specific set of quantum operations to his half of the entangled pair (qubit C). These operations depend on the classical bits received and are used to transform qubit C into the teleported state that was originally on qubit A.
By following these steps, the quantum state of qubit A is essentially "teleported" onto qubit C, which is in Bob's possession. However, it's important to note that the actual quantum state of qubit A is destroyed in the process.
The key role of the maximally entangled state (Bell pair) in quantum teleportation is to provide the necessary quantum correlations between the sender (Alice) and the receiver (Bob). The projection onto the maximally entangled state during the Bell measurement step ensures that the measurement outcomes obtained by Alice are correlated with the quantum state of the particle to be teleported. These outcomes are then used to guide the conditional operations performed by Bob to reconstruct the original state on his qubit.
In summary, the projection onto a maximally entangled state in quantum teleportation refers to the initial entanglement between the sender and receiver's particles, which facilitates the transfer of quantum information from one location to another.