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Advances in high-dimensional quantum entanglement

Nature Reviews Physics volume 2, pages 365–381 (2020)Cite this article

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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria

    Manuel Erhard, Mario Krenn & Anton Zeilinger

  2. Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, Austria

    Manuel Erhard, Mario Krenn & Anton Zeilinger

  3. Department of Chemistry and Computer Science, University of Toronto, Toronto, Ontario, Canada

    Mario Krenn

  4. Vector Institute for Artificial Intelligence, Toronto, Ontario, Canada

    Mario Krenn

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Real-time imaging of quantum entanglement: https://www.youtube.com/watch?v=wGkx1MUw2TU

Glossary

Qudit

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.

Fidelity

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.

Contextuality

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.

Hydex

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). https://doi.org/10.1038/s42254-020-0193-5

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