quantum teleportation

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Quantum teleportation is a protocol for transferring a quantum state, using a pre-distributed entangled pair and a classical channel. Unlike a fax, the state is not copied but transferred with the destruction of the original (due to the no-cloning theorem). Bell measurement yields one of four outcomes; these classical bits tell the receiver which unitary transformation to apply to reconstruct the state. The protocol does not transmit information faster than light, as the classical signal is limited to this speed.

History

The protocol was proposed in 1993 by Charles Bennett, Gilles Brassard, and colleagues. In 1997, groups led by Anton Zeilinger and Francesco De Martini first teleported photon states. The distance record—143 km—was set in 2012.

How it works

Alice and Bob each receive a particle from an entangled pair (e.g., two photons with entangled polarization). Alice combines particle X, whose state is to be transferred, with her part of the entangled pair and performs a Bell measurement. It yields one of four outcomes, encoded in two bits. Upon receiving these bits, Bob performs one of four operations on his particle, precisely restoring state X. The original state X is destroyed upon measurement.

💡 Without the classical signal with measurement results, the receiver sees only random noise. Therefore, teleportation does not violate causality and does not allow superluminal communication.

Quantum teleportation is a procedure for moving a quantum state without physical transfer of the carrier. Requirements: a maximally entangled pair (Bell state), a classical channel, and local operations. Initial state: |ψ⟩₁ = α|0⟩₁ + β|1⟩₁. Entangled pair: |Φ⁺⟩₂₃ = (|00⟩₂₃ + |11⟩₂₃)/√2. Bell measurement on qubits 1 and 2 projects qubit 3 into one of four states, which are corrected by Pauli operators (I, X, Z, XZ) according to the two classical bits, restoring |ψ⟩₁. The measurement does not reveal α and β. The protocol applies to any states but requires precise entanglement and protection from decoherence.

History

The concept was proposed in 1993 by Charles Bennett, Gilles Brassard, and co-authors. First experiments with photons were conducted in 1997 by groups led by Anton Zeilinger and Francesco De Martini. In 2012, teleportation was achieved over 143 km. In 2016, the Chinese satellite Mozi (Micius) teleported states between the satellite and Earth.

How it works

Teleportation uses entanglement and linearity. Bell measurement projects one pair into an entangled state, and the remote particle is corrected by a unitary operation. The necessity of a classical signal ensures causality. The impossibility of directly measuring the original state is related to the uncertainty principle. The protocol is a form of quantum error correction. Experimentally, photons with entangled polarization, time bins, or orbital angular momentum are used. Sources of entangled pairs include spontaneous parametric down-conversion; Bell measurement is performed with interferometers, and conditional operations with fast modulators.

|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)

|\Phi^\pm\rangle = \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle), |\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle)

Four orthonormal entangled states of two qubits; ± signs distinguish symmetric and antisymmetric combinations. Measurement on two qubits projects them into one of these states, yielding 2 bits of information.

I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}, XZ = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}

I — identity operation (do nothing); X — quantum NOT gate (flips 0↔1); Z — phase gate (changes sign of amplitude for |1⟩); XZ — sequential application of X and Z. Applied to Bob's qubit to restore the original state after receiving the classical bits.

Open problems & fun facts

Increasing the distance of teleportation while maintaining fidelity (problem of decoherence and losses in fiber or free space); Teleportation of complex multi-particle states or states of macroscopic objects (e.g., atomic ensembles); Creation of quantum repeaters for building a global quantum internet; Compatibility with various physical platforms (hybrid teleportation between atoms and photons)

💡 The term 'teleportation' was coined by writer Charles Fort in 1931. The idea of quantum teleportation was popularized after a Nature article (1997) with a photo of a 'Star Trek beam', although the protocol transfers only quantum information, not matter.

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quantum teleportation

History

How it works

History

How it works

History

How it works

Open problems & fun facts

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