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Advances in high-dimensional quantum entanglement

A Publisher Correction to this article was published on 14 July 2020

This article has been updated


Since its discovery, quantum entanglement has challenged some of the best established views of the world: locality and reality. Quantum technologies promise to revolutionize computation, communication, metrology and imaging. Here we review conceptual and experimental advances in complex entangled systems involving many multilevel quantum particles. We provide an overview of the latest technological developments in the generation and manipulation of high-dimensionally entangled photonic systems encoded in various discrete degrees of freedom such as path, transverse spatial modes or time–frequency bins. This overview should help to transfer various physical principles for the generation and manipulation from one degree of freedom to another and thus inspire new technical developments. We also show how purely academic questions and curiosity led to new technological applications. Fundamental research provides the necessary knowledge for upcoming technologies, such as a prospective quantum internet or the quantum teleportation of all information stored in a quantum system. Finally, we discuss some important problems in the area of high-dimensional entanglement and give a brief outlook on possible future developments.

Key points

  • High-dimensional quantum entanglement provides a playground for fundamental research and also leads to technological advances. Examples include stronger violations of local realistic world views that can be exploited to tolerate larger amounts of noise in quantum communication protocols.

  • Different physical concepts underlie the creation of high-dimensionally entangled photon pairs. Conservation laws result in correlations that if coherent in turn yield high-dimensionally entangled photon pairs. Multiple indistinguishable and coherent possibilities can be combined such that custom-tailored, high-dimensional entanglement is created.

  • Various physical and technical approaches on how to manipulate multilevel quantum states in different degrees of freedom (DoFs) are presented. Concepts used in one DoF may also be applied to other DoFs, inspiring new synergies that create new technologies.

  • Current advances in experimental methods for generating high-dimensional multiphoton entanglement enable future technologies, such as teleporting the complete quantum information stored in a single photon.

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Fig. 1: Curiosity-driven questions and technological applications of quantum mechanics, for varying system sizes.
Fig. 2: Entanglement creation and manipulation concepts for path degrees of freedom.
Fig. 3: Entanglement creation and manipulation for orbital angular momentum degrees of freedom.
Fig. 4: Entanglement creation and manipulation concepts for time and frequency bin encoding.
Fig. 5: Examples of the three classes of multiparticle entanglement in terms of dimension.
Fig. 6: Concept for performing 3D teleportation.

Change history

  • 14 July 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


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The authors thank S. Ecker and L. Bulla for insightful discussions related to time-bin entanglement. This work was supported by the Austrian Academy of Sciences (ÖAW), University of Vienna via the project QUESS and the Austrian Science Fund (FWF) with SFB F40 (FOQUS). M.E. acknowledges support from FWF project W 1210-N25 (CoQuS). M.K. acknowledges support from FWF via the Erwin Schrödinger fellowship number J4309.

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Correspondence to Manuel Erhard or Mario Krenn or Anton Zeilinger.

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Related links

Real-time imaging of quantum entanglement:



A qudit describes a d-dimensional quantum system. Qutrits and ququarts describe quantum states with three and four dimensions, respectively.

Positive–intrinsic–negative diodes

(PIN diodes). Light-sensitive diodes especially used for homodyne and heterodyne detection of many-photon states, such as coherent states.


The overlap between two quantum states.

Graph states

These are especially useful in the quantum information context to describe entangled multiqubit or qudit states with mathematical framework of graphs, where vertices describe qubits and edges interactions between pairs of them.

Standard quantum limit

The limit given in optical interferometric measurement using coherent laser light. One way it can be circumvented is by using squeezed states of light.


This means that the approach of ascribing pre-existing values to a quantum measurement results in a dependence of these values on other independent measurements that can be performed on the same system.

Normal operators

Linear operators on a complex Hilbert space that commute with their own Hermitian adjoint are called normal operators. Examples of normal operators are Hermite, unitary or skew operators.


A special CMOS-compatible material with a low χ3 nonlinear coefficient, but capable of hosting nonlinear optical effects such as spontaneous four-wave mixing in a high Q-value cavity environment. Alternatively, silicon nitride-based microring cavities are used.

CNOT gates

These describe two-qubit quantum gates, where the state of the control qubit (0/1) controls the transformation (nothing/bit-flip) performed on the target qubit.

Procrustean filtering

A filtering technique that removes part of the quantum state by introducing loss to match a desired state.

Dicke state

A Dicke state describes a multi-qubit quantum state that is an equal superposition of all combinations with k excitations.

W state

The W state is an n-qubit quantum state \(| \psi \rangle \) with an equal superposition of n terms, where each term has exactly one excited state \(| 1\rangle \): \(\begin{array}{l}| \psi \rangle =1\,/\,\sqrt{n}(| 100\cdots 0\rangle +| 0100\cdots 0\rangle \\ \,\,\,+\cdots +| 000\cdots 1\rangle ).\end{array}\)

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Erhard, M., Krenn, M. & Zeilinger, A. Advances in high-dimensional quantum entanglement. Nat Rev Phys 2, 365–381 (2020).

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