Algorithms · Entanglement and communication
Quantum teleportation
A communication primitive that makes entanglement, measurement, and classical feed-forward explicit.
Strong empiricalUpdated
A small worked example, computed in your browser. It is not a result from this record's papers.
Teleportation, deferred-measurement form
3 qubits, teleporting RY(π/3)|0⟩ from qubit 0 to qubit 2, with the corrections applied as controlled gates instead of classically controlled ones after a measurement.
Step 1 of 7 · RY(π/3)
⟨Z₂⟩ after this step1.00
Prepares the state to teleport on qubit 0: RY(π/3)|0⟩.
Probability spreads from 1 outcome to 2.
Starts a Bell pair between qubit 1 (Alice's half) and qubit 2 (Bob's half).
Probability spreads from 2 outcomes to 4.
Completes the Bell pair.
Probability moves: 2 outcomes appear that had none, 2 drop to zero, 4 carry probability now. Up: 110 0.0% → 37.5%. Down: 010 37.5% → 0.0%, 011 12.5% → 0.0%. This is the step that entangles the qubits: from here on no single qubit has a state of its own, only the register as a whole does.
The first half of Alice's Bell measurement on her two qubits (0 and 1), ordinarily followed by an actual measurement.
Probability moves: 2 outcomes appear that had none, 2 drop to zero, 4 carry probability now. Up: 011 0.0% → 12.5%, 101 0.0% → 12.5%. Down: 001 12.5% → 0.0%.
The second half of Alice's Bell measurement.
Probability spreads from 4 outcomes to 8.
The correction that would classically depend on Alice's qubit-1 outcome, applied instead as a genuine controlled gate (the 'deferred measurement' trick).
Probability moves between the same 8 outcomes. Up: 010 6.3% → 18.8%, 011 6.3% → 18.8%. Down: 110 18.8% → 6.3%.
The correction that would classically depend on Alice's qubit-0 outcome, applied the same way.
The outcome probabilities do not move at all. What this step changes is phase — 1 distinct relative phase across the state now — which no measurement can see until a later step turns it back into probability. The entanglement comes apart here: each qubit has a state of its own again.
Readout Qubit 2's marginal state matches RY(π/3)|0⟩ exactly: ⟨Z⟩ = cos(π/3) = 0.5. The state teleported across without qubit 0 and qubit 2 ever directly interacting.
Open in Studio- Steps3
- Wires3
- Qubits3
- Classical bits2
- Shared resourceBell pair
- Papers1
A part this method uses, worked through
This page says Bell pair
— here is a concrete, runnable instance of it.
A Bell pair
2 qubits, preparing (|00⟩ + |11⟩) / √2.
Where it ends up
- 0050%
- 1150%
Measuring both qubits always gives 00 or 11, each about half the time, and never 01 or 10.
Open this part in StudioTeleportation moves an unknown qubit state using a shared Bell pair and two classical bits. The protocol is a foundation for quantum networking and gate teleportation, not a replacement for classical communication.
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
Teleportation moves an unknown state from Alice to Bob using one shared Bell pair and two classical bits. Alice holds and her half of ; she applies CX then to the pair and measures both in the computational basis, obtaining classical bits . Before measurement the three-qubit state can be written as an equal superposition over Alice's four outcomes, each pairing a Bell-basis result with a specific Pauli acting on Bob's qubit: . Bob applies to undo that Pauli and recovers exactly — the ideal-circuit result this record checks on a toy state. No information travels faster than light: Bob's qubit is maximally mixed until the two classical bits arrive, and the protocol consumes (does not clone) the input state, consistent with the no-cloning theorem.
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
- Qubits
- 3
- Classical bits
- 2
- Shared resource
- Bell pair
- Input
- Unknown |ψ⟩
- Output
- Recovered |ψ⟩
- No-cloning
- Input consumed
Bellon Alice Bell half, Bob Bell halfBell meas.on input |ψ⟩, Alice Bell halfX/Z feed-forwardon Bob Bell half
Quantum vs classical
Classical baseline
Direct classical transmission of a known description, or physical transport of a classical bit; an unknown quantum state cannot be copied into a classical message of fixed size.
Quantum claim
Transfers an unknown qubit state using one shared entangled pair and two classical bits, with the input state consumed.
How to compare
Network latency, entanglement generation, memory lifetime, fidelity, and feed-forward control are the real system metrics.
Nobody has reviewed this record for gaps yet.
from qiskit import QuantumCircuit
qc = QuantumCircuit(3, 2)
# Prepare an input state and a shared Bell pair.
qc.h(1)
qc.cx(1, 2)
qc.cx(0, 1)
qc.h(0)
qc.measure([0, 1], [0, 1])
# Apply classically controlled corrections to q2.
FINAL_CIRCUIT = qcThe final corrections are shown as a boundary because the exact dynamic-circuit syntax varies by backend.
Related entries
- Bell state measurement
Basic circuits
- Hadamard gate
Gates
- Surface-code memory and biased-noise decoding
Operators
References
- Teleporting an unknown quantum state via dual classical and EPR channels
Charles H. Bennett et al. · 1993
Original teleportation protocol using an entangled pair and two classical bits.