Everything about Quantum Teleportation totally explained
Quantum teleportation or
entanglement-assisted teleportation is a quantum
protocol by which
quantum information can be transmitted utilizing a classical
communication channel and an entangled
pair of qubits. The sender's original qubit is destroyed in the process, as required by the
no cloning theorem. The entangled pair of qubits is also separated.
Quantum teleportation doesn't transport
energy or
matter, nor does it allow communication of information at
superluminal (faster than light) speed, but is useful for quantum communication and
computation.
Motivation
The two parties are
Alice (A) and Bob (B), and a
qubit is, in general, a
superposition of
quantum state labelled
and
. Equivalently, a qubit is a unit vector in two-dimensional
Hilbert space.
Suppose Alice has a qubit in some arbitrary quantum state
. Assume that this quantum state isn't known to Alice and she'd like to send this state to Bob. Ostensibly, Alice has the following options:
- She can attempt to physically transport the qubit to Bob.
- She can broadcast this (quantum) information, and Bob can obtain the information via some suitable receiver.
- She can perhaps measure the unknown qubit in her possession. The results of this measurement would be communicated to Bob, who then prepares a qubit in his possession accordingly, to obtain the desired state. (This hypothetical process is called classical teleportation.)
Option 1 is highly undesirable because quantum states are fragile and any perturbation en route would corrupt the state.
The unavailability of option 2 is the statement of the
no-broadcast theorem.
Similarly, it has also been shown formally that classical teleportation, aka. option 3, is impossible; this is called the
no teleportation theorem. This is another way to say that quantum information can't be measured reliably.
Thus, Alice seems to face an impossible problem. A solution was discovered by Bennet et al. (see reference below.) The parts of a maximally entangled two-qubit state are distributed to Alice and Bob. The protocol then involves Alice and Bob interacting locally with the qubit(s) in their possession and Alice sending two classical bits to Bob. In the end, the qubit in Bob's possession will be in the desired state.
A summary
Assume that Alice and Bob share an entangled qubit AB. That is, Alice has one half, A, and Bob has the other half, B. Let C denote the qubit Alice wishes to transmit to bob.
Alice applies a unitary operation on the qubits AC and measures the result to obtain two classical bits. In this process, the two qubits are destroyed. Bob's qubit, B now contains information about C however the information is somewhat randomized. More specifically, Bob's qubit B is in one of four states uniformly chosen at random and Bob can't obtain any information about C from his qubit.
Alice provides her two measured qubits, which indicate which of the four states Bob possesses. Bob applies a unitary transformation which depends on the qubits he obtains from Alice, transforming his qubit into an identical copy of the qubit C.
The result
Suppose Alice has a qubit that she wants to teleport to Bob. This qubit can be written generally as:
Our quantum teleportation scheme requires Alice and Bob to share a maximally
entangled state beforehand, for instance one of the four
Bell states
» Further Information
Get more info on 'Quantum Teleportation'.
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