What is quantum teleportation?

What actually gets teleported

Quantum teleportation moves information, not objects. Alice has a qubit in some state α|0⟩ + β|1⟩ that she may not even know. At the end, a qubit in Bob's lab is in exactly that state, and Alice's qubit is not. The particles stay where they are.

That matters because you cannot simply measure a qubit and send the numbers. A measurement returns one bit, 0 or 1, and destroys the amplitudes α and β. And you cannot copy an unknown quantum state at all: the no-cloning theorem (Wootters, Zurek and Dieks, 1982) forbids it. Teleportation is the way round both problems.

What you need

• One shared entangled pair. Alice and Bob each hold one qubit of a Bell pair, (|00⟩ + |11⟩)/√2, prepared in advance. (See what is quantum entanglement?)
• A classical channel. Any ordinary way to send two bits: a phone call, a network packet.
• A few quantum gates. A CNOT and a Hadamard gate on Alice's side, and an X and a Z on Bob's.

How it works, step by step

1. Entangle the message with the pair. Alice applies a CNOT from her message qubit to her half of the Bell pair, then a Hadamard gate to the message qubit.
2. Measure. Alice measures both of her qubits. She gets one of four results, 00, 01, 10 or 11, each with probability 1/4, whatever the state was. The result says nothing about α or β.
3. Send two bits. Alice tells Bob her two-bit result over the classical channel.
4. Fix up. Depending on the two bits, Bob applies nothing, an X gate, a Z gate, or both. His qubit is now in the state α|0⟩ + β|1⟩.

The trick is in step 1. Before Alice measures, the three-qubit state can be rewritten as four equal pieces, one for each possible measurement result, and in each piece Bob's qubit already holds α and β, just scrambled by a known flip. The measurement picks one piece at random, and the two bits tell Bob which flip to undo.

Teleportation in Python

This simulation runs the whole protocol on three qubits with NumPy. It picks a random state, teleports it, and checks Bob's qubit against the original for each of Alice's four possible results. A fidelity of 1 means the states are identical.

import numpy as np

rng = np.random.default_rng(7)

# The state Alice wants to send: a random qubit a|0> + b|1>.
psi = rng.normal(size=2) + 1j * rng.normal(size=2)
psi /= np.linalg.norm(psi)

I = np.eye(2)
X = np.array([[0, 1], [1, 0]])
Z = np.array([[1, 0], [0, -1]])
H = np.array([[1, 1], [1, -1]]) / np.sqrt(2)

def on(gate, qubit):
    """Apply a one-qubit gate to qubit 0, 1 or 2 of a 3-qubit register."""
    ops = [I, I, I]
    ops[qubit] = gate
    return np.kron(np.kron(ops[0], ops[1]), ops[2])

def cnot(control, target):
    U = np.zeros((8, 8))
    for i in range(8):
        bits = [(i >> 2) & 1, (i >> 1) & 1, i & 1]
        if bits[control]:
            bits[target] ^= 1
        U[(bits[0] << 2) | (bits[1] << 1) | bits[2], i] = 1
    return U

# Qubit 0 holds psi. Qubits 1 (Alice) and 2 (Bob) share a Bell pair.
bell = np.array([1, 0, 0, 1]) / np.sqrt(2)
state = np.kron(psi, bell)

# Alice: CNOT from her message qubit onto her half of the pair, then H.
state = on(H, 0) @ cnot(0, 1) @ state

# Alice measures qubits 0 and 1. Look at all four possible results.
for m0 in (0, 1):
    for m1 in (0, 1):
        rows = [(m0 << 2) | (m1 << 1) | b for b in (0, 1)]
        bob = state[rows]
        p = np.vdot(bob, bob).real
        bob = bob / np.sqrt(p)
        # Bob's fix-up, using Alice's two classical bits.
        if m1:
            bob = X @ bob
        if m0:
            bob = Z @ bob
        fidelity = abs(np.vdot(psi, bob)) ** 2
        print(f"Alice reads {m0}{m1} (chance {p:.2f}) -> Bob's qubit matches: fidelity {fidelity:.6f}")

Alice reads 00 (chance 0.25) -> Bob's qubit matches: fidelity 1.000000
Alice reads 01 (chance 0.25) -> Bob's qubit matches: fidelity 1.000000
Alice reads 10 (chance 0.25) -> Bob's qubit matches: fidelity 1.000000
Alice reads 11 (chance 0.25) -> Bob's qubit matches: fidelity 1.000000

All four outcomes are equally likely, and in every one of them Bob ends up with exactly the state Alice started with.

Why it is not faster than light

Until Bob receives Alice's two bits, his qubit is in one of four scrambled states with equal probability, and on average that is completely random: nothing he measures tells him anything about α or β. The two bits travel at the speed of light or slower, so the state can never arrive faster than a signal could. Entanglement creates correlations, but it cannot carry a message on its own.

Is it really teleportation?

The name is accurate in one narrow sense: the state disappears in one place and reappears in another without passing through the space between. It is nothing like science-fiction teleportation of objects or people. What moves is the description of one qubit, and it costs one entangled pair and two classical bits every time.

Milestones

• 1993: Charles Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres and William Wootters propose the protocol.
• 1997–1998: The first experimental demonstrations, with photons, by Anton Zeilinger's group in Innsbruck and by Francesco De Martini's group in Rome.
• 2017: The Chinese satellite Micius teleports the states of photons from a ground station in Tibet to orbit, over distances of up to about 1,400 km.
• 2025: Researchers at the University of Oxford use teleportation to run a logic gate between two separate ion-trap quantum computers about two metres apart, an early step towards networked quantum computers.

Why it matters for quantum computers

Teleportation is not just a physics demonstration. It is a working part of where quantum technology is heading:

• Quantum networks. Sending qubits down long fibres loses them. Quantum repeaters instead spread entanglement hop by hop and use teleportation to pass states along.
• Linking quantum chips. Building one enormous chip is hard. Connecting smaller modules and teleporting states or gates between them is one of the main plans for scaling up.
• Error-corrected computing. Some of the operations that are hardest to do reliably in quantum error correction are carried out by "gate teleportation", a variant of the same protocol.

Frequently asked questions

Can quantum teleportation send information faster than light?

No. Bob needs two ordinary bits from Alice before his qubit holds the state, and those bits cannot travel faster than light. Without them, his qubit looks completely random.

Does quantum teleportation copy the qubit?

No. Alice's measurement destroys the state on her side, so there is only ever one copy. That is required by the no-cloning theorem, which says an unknown quantum state cannot be copied.

Could people ever be teleported this way?

Not with anything known today. Teleportation moves the quantum state of individual particles, one entangled pair and two classical bits per qubit, and the receiving side must already have the matter to put the state into.