Quantum teleportation: what moves and what does not

Short answer: Quantum teleportation transfers the state of a qubit from a sender to a receiver using a shared entangled pair plus two bits of ordinary classical communication. No matter moves, and nothing travels faster than light, because the receiver cannot finish the job until the classical bits arrive. It is a well-established textbook protocol, described here at explainer level only.

What exactly is being moved?

The term "teleportation" is often misunderstood as implying the physical transport of matter, similar to science fiction concepts where objects are disassembled and reassembled elsewhere. However, in quantum information theory, matter is not teleported. What is actually transmitted is quantum information. Specifically, the protocol allows a sender, often labeled Alice, to transmit a qubit to a receiver, Bob, by utilizing a shared entangled quantum state. This shared resource is referred to as an e-bit. The process requires two bits of classical communication in addition to the entangled pair. The goal is to transfer the specific quantum state encoded in a qubit, not the physical atom or photon that carries it.

In practical terms, if Alice possesses a qubit containing unknown information, she does not need to send the physical carrier through a conduit to Bob. Instead, she transfers the state of that qubit. The distinction is critical: the physical particle remains with Alice, while the quantum state is recreated at Bob’s location. In physicist John Preskill's example in Quanta Magazine, a qubit encoded in an atom in California is delivered as information to someone in New York, while the atom itself stays where it is. The identity of the state is what matters, not the material substrate.

How does the protocol function without knowing the state?

A fundamental challenge in quantum mechanics is that one cannot simply measure an unknown quantum state to learn its properties and then send that information to a receiver. If Alice were to measure the qubit to determine its amplitudes, she would destroy the quantum state due to the measurement process. Furthermore, in general, Alice does not know the specific amplitudes of the state she holds. There is no reason to suppose she knows the identity of her quantum state.

The teleportation protocol solves this by allowing the transfer of the state even when neither Alice nor Bob knows the identity of the state. Alice performs a joint measurement on the qubit she wishes to send and her half of the shared entangled pair. This measurement does not reveal the state of the original qubit to Alice; instead, it projects the pair into one of several possible states. The outcome of this measurement is one of four possibilities, which can be encoded in two classical bits. Alice sends these two bits to Bob via a classical channel, such as the internet.

Upon receiving the two bits, Bob knows which operation to perform on his half of the entangled pair. By applying the appropriate correction based on the classical message, Bob’s qubit becomes identical to the original state held by Alice. The original state at Alice’s location is destroyed in the process, ensuring that there is no duplication of the quantum information, which is forbidden by the no-cloning theorem.

Why is entanglement necessary?

The protocol requires a shared entangled state, specifically an e-bit, between the sender and the receiver. This entanglement can be established in advance. For instance, Alice and Bob could have been in the same location in the past, prepared the qubits in an entangled state, and then each went their own way with their qubit in hand. Alternatively, a third party or a complex distribution process could have facilitated the creation of the entangled pair.

Without this pre-shared entanglement, the protocol cannot function. Classical communication alone is insufficient to transmit an unknown quantum state. If Alice were to attempt to send the state by simply telling Bob the amplitudes, she would first need to know them, which is impossible for an arbitrary unknown state without destroying it. The entangled pair acts as a resource that links the two locations, allowing the quantum information to be transferred through the combination of local operations and classical communication. The entanglement provides the non-classical correlation necessary to complete the transfer.

What are the limitations and misconceptions?

It is crucial to understand that quantum teleportation does not involve faster-than-light signaling. The protocol requires the transmission of two bits of classical information from Alice to Bob. Since classical information cannot travel faster than the speed of light, the teleportation process is limited by the speed of light. Bob cannot reconstruct the state until he receives the classical message. Therefore, no information is transmitted instantaneously.

Additionally, the protocol does not transport matter. The physical particle associated with the original state remains with the sender. Only the quantum state is transferred. This distinction is vital for avoiding misconceptions about the physical implications of the technology. The process is a method of state transfer, not matter transport.

The complexity of the protocol also means that it is not trivial to implement. The steps involved are sufficiently simple to lay out theoretically, but the practical realization requires precise control over quantum states and measurements. The fact that the protocol works even when the state is unknown is a notable result, but it does not imply that the technology is simple or that it bypasses fundamental physical limits. It remains a protocol for transferring quantum information, subject to the constraints of quantum mechanics and relativity.

FAQ

Does quantum teleportation move matter?

No. As the Qiskit course puts it, matter is not teleported; what is teleported is quantum information.

What does the protocol need?

A shared entangled pair (one e-bit) between sender and receiver, plus two bits of classical communication.

Can it send information faster than light?

No. The receiver needs the two classical bits to apply the right correction, and those travel no faster than light.

Does the sender need to know the state?

No. Teleportation works even when neither the sender nor the receiver knows the identity of the state.

Why not just measure the qubit and send the result?

Measuring an unknown state would disturb it, and in general the sender does not know the amplitudes. Entanglement plus classical bits gets around this.