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Advances in Quantum Teleportation
Stefano Pirandola, Jens Eisert, Christian Weedbrook, Akira Furusawa, Samuel L. Braunstein
TL;DR
Quantum teleportation is a central entanglement-based protocol whose theory, variants, experiments, and technological implementations span quantum communication, computing, and networks. This review synthesizes these developments across physical platforms and identifies implementation challenges and future directions.
Problem
Quantum teleportation must be understood as both a foundational entanglement-based protocol and a practical building block across diverse quantum technologies.
Method
The paper reviews teleportation theory and variants, surveys experiments across platforms, and analyzes their technical advantages, disadvantages, and future implementations.
Results
Quantum teleportation has been demonstrated across photonic, optical, atomic, trapped-atom, NMR, and solid-state systems, with applications spanning repeaters, computing, and networks.
Takeaways & Limitations
Teleportation remains a key primitive whose future development depends on matching platforms and quantum memories to communication, computing, and networking requirements.
Abstract
from arXiv · showhide
Quantum teleportation is one of the most important protocols in quantum information. By exploiting the physical resource of entanglement, quantum teleportation serves as a key primitive in a variety of quantum information tasks and represents an important building block for quantum technologies, with a pivotal role in the continuing progress of quantum communication, quantum computing and quantum networks. Here we review the basic theoretical ideas behind quantum teleportation and its variant protocols. We focus on the main experiments, together with the technical advantages and disadvantages associated with the use of the various technologies, from photonic qubits and optical modes to atomic ensembles, trapped atoms, and solid-state systems. Analysing the current state-of-the-art, we finish by discussing open issues, challenges and potential future implementations.
From Science Fiction to Reality
Quantum teleportation transfers an unknown quantum state using shared entanglement and classical communication, with Bob applying a measurement-dependent correction. The protocol underlies major quantum-information applications and has been demonstrated across diverse platforms.
- From Science Fiction to Reality: Quantum teleportation requires shared entanglement and classical communication, excluding superluminal communication.Alice measures the input jointly with her entangled subsystem, then Bob reconstructs the state using the communicated result.
- From Science Fiction to Reality: Quantum teleportation supports quantum repeaters, gate teleportation, measurement-based computing, port-based teleportation, and quantum-network architectures.It has also been used to explore theoretical settings such as closed time-like curves and black-hole evaporation.
- From Science Fiction to Reality: Laboratory demonstrations span photonic qubits, NMR, optical modes, atomic ensembles, trapped atoms, and solid-state systems.Experiments have achieved notable teleportation distances and begun attempts to scale to more complex quantum systems.
- A. Quantum Teleportation of Qubits and Discrete Variables: In the qubit protocol, Alice performs Bell detection and Bob applies the corresponding Pauli operator to recover the input state.The ideal protocol uses a Bell pair and achieves an exact replica with fidelity F = 1.
- A. Quantum Teleportation of Qubits and Discrete Variables: Fclass = 2/3 is the classical benchmark for arbitrary qubit inputs, so quantum-resource use requires fidelity F > Fclass.Typical experiments use pure input states from limited alphabets, including the six poles of the Bloch sphere.
- A. Quantum Teleportation of Qubits and Discrete Variables: Teleportation extends to any finite dimension d by replacing Pauli operators with a unitary basis and distinguishing d2 classical outcomes.The input must be unknown, and successful teleportation preserves correlations with any third party.
B. Quantum Teleportation of Continuous Variables
Continuous-variable teleportation applies to infinite-dimensional systems, typically optical bosonic modes. The standard protocol uses an EPR resource, a quadrature Bell measurement, and a conditional displacement, with fidelity determined by entanglement.
- B. Quantum Teleportation of Continuous Variables: Continuous-variable teleportation extends the protocol to infinite-dimensional systems, typically realized as optical bosonic modes.Other possible systems include optomechanical modes and collective spins of atomic ensembles.
- B. Quantum Teleportation of Continuous Variables: The standard optical protocol uses a two-mode squeezed vacuum EPR state and an unknown coherent-state input.Alice mixes the input and resource modes on a balanced beam splitter and homodynes conjugate quadratures.
- B. Quantum Teleportation of Continuous Variables: Alice communicates k = q−+ ip+ after the Bell measurement, and Bob performs a conditional displacement on mode B.The displacement implements the feed-forward correction associated with the measured quadratures.
Variants of Teleportation
Quantum teleportation is an important primitive with extensions that serve both as quantum-technology protocols and as conceptual tools for theoretical models.
- Variants of Teleportation: Teleportation has been extended into protocols with practical quantum-technology roles and variants valued primarily for conceptual applications.The paper introduces these variants as recent developments beyond the basic scheme.
A. Entanglement Swapping and Quantum Repeaters
Teleportation variants distribute entanglement, connect remote parties, and support assisted or simultaneous transmission in multipartite networks. Entanglement swapping combined with distillation forms the basis of quantum repeaters.
- A. Entanglement Swapping and Quantum Repeaters: Entanglement swapping transfers entanglement when a middle relay performs the Bell detection on systems received from two locally entangled pairs.Alice and Bob retain one system each while sending the other systems to Charlie.
- A. Entanglement Swapping and Quantum Repeaters: Entanglement swapping and distillation form the basis of quantum repeaters for distributing entanglement over large distances.After maximal entanglement is distilled along a repeater chain, teleportation transfers quantum information between end-users.
- A. Entanglement Swapping and Quantum Repeaters: In a three-party assisted network, a local measurement by Charlie can improve teleportation fidelity from Alice to Bob.The operation must increase the bipartite entanglement of the remaining parties.
- A. Entanglement Swapping and Quantum Repeaters: For qubits, GHZ-state assisted teleportation is equivalent to quantum secret sharing, requiring Charlie’s assistance for Bob to recover Alice’s information.Continuous-variable assisted networks can use Gaussian states generated with squeezed vacua and beam splitters.
- A. Entanglement Swapping and Quantum Repeaters: Unassisted teleportation to two recipients is quantum telecloning, with fidelity bounded by 5/6 for qubits and 2/3 for coherent states.Charlie receives a copy rather than assisting Alice’s transmission to Bob.
C. Quantum Gate Teleportation and Quantum Computing
Quantum teleportation extends beyond state transfer to gate implementation, cluster-state computing, and port-based protocols, while experiments are assessed by completeness, independent verification, and fidelity above classical limits.
- C. Quantum Gate Teleportation and Quantum Computing: Gate teleportation implements unitary manipulation by preparing entangled auxiliary states, measuring locally, and applying single-qubit operations.
- C. Quantum Gate Teleportation and Quantum Computing: Cluster-state computing teleports a node’s state onto another node while concurrently applying a desired quantum gate.
- C. Quantum Gate Teleportation and Quantum Computing: Port-based teleportation lets Bob select the output port identified by Alice’s measurement without applying a correction.
- C. Quantum Gate Teleportation and Quantum Computing: Port-based teleportation is mainly important for conceptual studies because it requires large entanglement resources.
- Experimental requirements: Complete experiments require an arbitrary input, independent input preparation and output verification, complete Bell detection, and fidelity above the classical threshold.
- Experimental requirements: Failure of complete Bell detection produces post-selected teleportation with Bell-efficiency bounding the overall success probability, whereas complete detection enables unconditional teleportation.
A. Photonic Qubits
Photonic-qubit teleportation has progressed from post-selected, probabilistic demonstrations to long-distance free-space links and increasingly complex or integrated implementations. Its main limitations remain incomplete Bell detection, resource overhead, and experimental post-processing constraints.
- Bell detection: Linear optics and photodetection distinguish at most two of four Bell states, limiting photonic-qubit Bell-efficiency to 50%.Ancillary qubits can theoretically raise the efficiency toward 100%, but require additional quantum resources.
- Early demonstrations: Early photonic-qubit experiments achieved 25% Bell-efficiency in Innsbruck and later 50% over a 600 m fibre link.The Innsbruck implementation also raised concerns because Bob’s teleported qubit had to be detected, making teleportation effectively post-dicted.
- Telecom and relay experiments: Time-bin qubits were teleported over 2 km of telecom fibre between 1.3 µm and 1.55 µm photons, with 25% Bell-efficiency and ≃81% fidelity.The experiment was later extended to a relay configuration involving a third-party Bell detection.
- Long-distance teleportation: Free-space polarisation-qubit experiments reached distances suggesting that atmospheric links and ground-to-satellite implementations are technologically feasible.One 100 km ground-level link used 50% Bell-efficiency, fidelity ≳80%, and channel attenuation of 35–53 dB.
- Integration and composite systems: Integrated photonic teleportation demonstrated a dual-rail qubit on a configurable chip, but Bell detection was only 1/27 and the 89% fidelity was extrapolated from simulated feed-forward.Other work simultaneously teleported a photon’s spin and orbital angular momentum with 57–68% fidelity, above the 40% classical threshold.
B. Nuclear Magnetic Resonance
Nuclear magnetic resonance provides a teleportation platform in which complete Bell detection is achievable. A demonstration used nuclear spins in labelled trichloroethylene molecules and averaged results over an ensemble.
- NMR implementation: NMR teleportation achieved complete Bell detection using the nuclear spins of two carbon nuclei and one hydrogen nucleus.Entanglement between C1 and H enabled teleportation from C2 to H in an ensemble of labelled trichloroethylene molecules.
C. Optical Modes
Optical-mode continuous-variable teleportation makes Bell detection highly efficient with linear optics, while finite squeezing prevents ideal fidelity. Hybrid CV–DV schemes combine the detection advantages of CV systems with the fidelity advantages of discrete-variable encoding.
- Continuous-variable Bell detection: Continuous-variable Bell detection uses a balanced beamsplitter and two conjugate homodyne detectors, with efficiency approaching 100%.The approach satisfies the stated teleportation conditions when input states belong to an appropriate restricted class.
- Experimental performance: Optical-mode experiments reached fidelities of ≃70% and ≃76%, beating the no-cloning bound and transferring nonclassical features such as non-positive Wigner functions.Other coherent-state experiments reported fidelities of ≃61% and ≃64% under phase or amplitude-and-phase modulation.
- Resource limitation: Finite squeezing prevents continuous-variable teleportation fidelity from reaching 100%, because maximally entangled states require infinite resources.Realistic EPR states use finitely squeezed modes generated through parametric downconversion and a balanced beamsplitter.
- Hybrid schemes: Hybrid CV–DV teleportation of a photonic time-bin qubit aims to combine near-complete Bell detection with high discrete-variable fidelity.Using moderate squeezing, the demonstrated broadband approach can achieve fidelities ≳80%.
- Technology outlook: Optical modes support communication integration through high-performance homodyne detectors and commercially available electro-optical components, although distance limits remain unclear.The prior continuous-variable experiments were table-top, while increased loss may make long-distance teleportation more fragile.
D. Atomic Ensembles
Atomic ensembles support both continuous-variable and discrete-variable teleportation between light and matter or between matter systems, with storage capabilities relevant to quantum networks.
- Light-to-matter teleportation: The first light-to-matter experiment teleported coherent optical-mode states onto the collective spin of approximately 10^12 room-temperature Caesium atoms using continuous variables.Collective transverse spin components were described by quadrature operators.
- Light-to-matter teleportation: Unconditional light-to-matter teleportation achieved fidelity ≳58% for an input alphabet of coherent states.The atomic ensemble offered sub-second coherence times and millisecond storage times.
- Matter-to-matter teleportation: Unconditional matter-to-matter continuous-variable teleportation between two Caesium ensembles achieved fidelity ≳55%.The deterministic protocol also teleported time-evolving spin states, realizing stroboscopic teleportation.
- Discrete-variable teleportation: Discrete-variable light-to-matter teleportation with cold Rubidium ensembles reached ≃78% fidelity over 7 m in fibre, with ≃8 µs storage.The 50% Bell efficiency made this protocol probabilistic.
E. Trapped Atomic Qubits
Trapped atomic qubits provide high-fidelity teleportation and long storage times, while photonic interfaces extend separation beyond micrometre-scale traps at the cost of probabilistic operation and technical trade-offs.
- Local trapped ions: Trapped ions provide unconditional qubit teleportation with very long storage times but distances limited by short-range Coulomb interactions.These properties make them useful as quantum memories for teleportation-based quantum-computing subroutines.
- Local trapped ions: Three trapped Be^+ and Ca^+ ions achieved fidelities of ≃78% and ≃83%, respectively, with the latter improving on the earlier experiment.The ions were confined in linear Paul traps with inter-ion spacings of 3 µm and 5 µm.
- Remote trapped atoms: Photonic-matter interfaces extend trapped-atom separation beyond micrometres but practical linear optics provides incomplete Bell detection.This produces a trade-off between distance, probabilistic operation, photon collection, and coherence time.
- Remote trapped atoms: Probabilistic teleportation reached ≃90% fidelity between Ytterbium ions and ≃88% between neutral Rubidium atoms in distant optical cavities.The Ytterbium setup had long coherence times but inefficient free-space photon collection, whereas cavities improve collection at the expense of shorter coherence times.
F. Solid State Systems
Solid-state platforms demonstrate probabilistic photonic-to-memory teleportation and unconditional matter-to-matter teleportation across quantum-dot, crystal, superconducting, and diamond systems.
- Photonic-to-memory teleportation: Photonic frequency qubits were probabilistically teleported onto charged quantum-dot electron spins over 5 m with ≃78% fidelity.The spin coherence time was extended to ≃13 ns using spin echo.
- Photonic-to-memory teleportation: A telecom-wavelength polarisation qubit was probabilistically teleported to a rare-earth crystal memory with ≃89% fidelity and 50 ns photon storage.A relay configuration used two 12.4 km fibres, with slightly reduced fidelity for one long-distance state.
- Matter-to-matter teleportation: Superconducting transmons separated by 6 mm achieved post-selected fidelity ≃81%, unconditional fidelity ≃77%, and real-time feed-forward fidelity ≃69%.The experiment operated at 10^4 Hz with microsecond coherence times.
- Matter-to-matter teleportation: Nitrogen-vacancy centres in diamond were teleported between spins separated by 3 m using complete Bell detection and real-time feed-forward.Entanglement swapping linked the centres through optical fields overlapped at a beamsplitter.
Discussion and Outlook
The review compares quantum teleportation technologies across quality factors and applications, identifying hybrid architectures and quantum memories as important directions while highlighting unresolved long-distance challenges.
- Technology comparison: No single quantum system excels across all quality factors, so technology choice depends on the intended teleportation application.The comparison considers Bell-state-analyzer efficiency, fidelity, distance, storage time, and related coherence properties.
- Quantum computing: Short-distance teleportation (≲1 m) for quantum-computing subroutines is promising with circuit QED, despite coherence times limited to ≲100 µs.Superconducting transmons offer deterministic, high-fidelity on-chip teleportation, real-time feed-forward, and scalable integration.
- Quantum communication: Optical modes could support metropolitan-scale communication at high rates and bandwidths, while hybrid approaches or non-Gaussian repeaters may extend distance at lower rates.The proposed metropolitan scale is a few kilometres; longer-distance implementations trade rate for reach.
- Long-distance teleportation: Beyond 100 km, polarisation qubits support low-rate teleportation over fibre and free-space links, but incomplete Bell detection currently makes the protocol probabilistic.This probabilistic operation is acceptable for some tasks but conflicts with communication settings requiring full preservation of input quantum information.
- Satellite links: Satellite implementations are technologically reachable, but beam spreading causes substantial loss; a two-downlink configuration is estimated at about 75 dB loss.The estimate assumes a 20 cm satellite aperture at ≃600 km and 1 m ground telescopes, compared with ≃80 dB at ground level.
- Quantum memories: Scalable quantum networks depend on quantum memories combining efficient radiation–matter interfaces, high write-read fidelity, long storage, and substantial bandwidth.Such memories could support entanglement distribution, teleportation-based communication, and coherent processing of stored quantum information.