# Quantum entanglement

**Quantum entanglement** is a property of a composite quantum system whose parts cannot be described independently, even when separated, so that measurements on the parts show correlations stronger than any shared classical information can produce. [Albert Einstein](https://www.edgepedia.org/albert-einstein) discussed the phenomenon with Boris Podolsky and [Nathan Rosen](https://www.edgepedia.org/nathan-rosen) in their 1935 [EPR paradox](https://www.edgepedia.org/epr-paradox), and Erwin Schrödinger, in a 1935 article, called it "the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought"<sup>[1](https://www.nobelprize.org/uploads/2026/05/advanced-physicsprize-2022-5.pdf)</sup>. Experiments beginning in the 1970s confirmed that these correlations are real, and the 2022 Nobel Prize in Physics was awarded to Alain Aspect, John Clauser, and Anton Zeilinger "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science"<sup>[2](https://www.nobelprize.org/prizes/lists/all-nobel-prizes/all/?gallery_style=page)</sup>.

| Key fact | Detail |
|---|---|
| Definition | A state of two or more systems that cannot be written as a product of independent states; measurements on one part determine the correlated outcome on another, however far apart<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup> |
| Archetypal state | The Bell state \( \vert \phi^+ \rangle = \tfrac{1}{\sqrt{2}} \vert 00\rangle + \tfrac{1}{\sqrt{2}} \vert 11\rangle \), viewed as one unit of entanglement, an "e-bit"<sup>[4](https://learning.quantum.ibm.com/course/basics-of-quantum-information/entanglement-in-action)</sup> |
| Foundational test | Bell inequalities (1964) distinguish quantum predictions from local hidden variables; experiments since 1972 violate them as quantum mechanics predicts<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup> |
| No faster-than-light signaling | Entanglement correlations cannot be harnessed for instantaneous communication; slightly stronger correlations would make communication complexity trivial<sup>[5](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.250401)</sup> |
| First applications | Link between entanglement and secure cryptographic key generation discovered in 1991; quantum teleportation first demonstrated in 1997<sup>[6](https://www.nature.com/articles/s41534-025-01072-3)</sup><sup> • </sup><sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup> |
| Recognition | 2022 Nobel Prize in Physics to Aspect, Clauser, and Zeilinger<sup>[2](https://www.nobelprize.org/prizes/lists/all-nobel-prizes/all/?gallery_style=page)</sup> |

## What entanglement is

When two particles are in an entangled state, a measurement of one particle immediately determines the result of an equivalent measurement on the other, without needing to check it. What distinguishes this from ordinary correlation is that the properties have no determined values before measurement: in the Nobel Foundation's illustration, the two "balls" are gray until one is looked at, whereupon one randomly turns black and the other white<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup>.

The simplest example is a pair of qubits, two-level quantum systems, in the [Bell state](https://www.edgepedia.org/bell-state) \( \vert \phi^+ \rangle \). An entangled state is one that cannot be represented as a tensor product of individual states for the two systems<sup>[7](https://quantum.cloud.ibm.com/learning/en/courses/utility-scale-quantum-computing/bits-gates-and-circuits)</sup>. IBM's quantum information course notes that a merely classically correlated, separable state such as the mixture \( \tfrac{1}{2} \vert 00 \rangle + \tfrac{1}{2} \vert 11 \rangle \) is not entangled, unlike the entangled Bell state \( (\vert 00 \rangle + \vert 11 \rangle)/\sqrt{2} \); entanglement refers specifically to non-classical quantum correlations, and the Bell state is treated as one unit of entanglement, an e-bit<sup>[4](https://learning.quantum.ibm.com/course/basics-of-quantum-information/entanglement-in-action)</sup><sup> • </sup><sup>[17](https://learn.microsoft.com/en-us/azure/quantum/concepts-entanglement)</sup>.

Entanglement can involve more than two particles and more than two levels per particle. Systems with more than two particles, all entangled, were first explored by [Anton Zeilinger](https://www.edgepedia.org/anton-zeilinger) and colleagues<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup>, and high-dimensional entanglement, in which each photon carries more than one bit of information in degrees of freedom such as path, orbital angular momentum, or time-frequency bins, is now an active research area<sup>[8](https://www.nature.com/articles/s42254-020-0193-5)</sup>.

## From paradox to Bell inequalities

The EPR argument of 1935 held that quantum mechanics does not provide a complete description of reality, and that a more complete description might work through particles carrying hidden information, later called local hidden variables, about measurement results<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup>. In 1964 [John Stewart Bell](https://www.edgepedia.org/john-stewart-bell) (1928–1990), a Northern Irish physicist working at CERN, showed that such theories predict correlations between repeated measurement results that must be lower than, or at most equal to, a specific value, now called Bell's inequality. [Quantum mechanics](https://www.edgepedia.org/quantum-mechanics) predicts higher correlations, so experiments can distinguish the two descriptions<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup>.

**Experimental violations.** [John Clauser](https://www.edgepedia.org/john-clauser) built an apparatus emitting pairs of entangled photons toward polarization filters, and in 1972, with doctoral student Stuart Freedman (1944–2012), obtained a clear violation of a Bell inequality agreeing with quantum mechanics<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup>. Early experiments had loopholes: detection was inefficient and the filter settings were fixed in advance, so an observer could question whether the setup selected only strongly correlated particles. [Alain Aspect](https://www.edgepedia.org/alain-aspect) refined the experiment over several iterations, registered photons that passed the filter and those that did not, and in the final variant switched the photons between two filters set at different angles after emission. With filters six meters away, the switch had to occur within a few billionths of a second, closing the locality loophole and giving a very clear result<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup>. Later work, including a landmark experiment honored with the Bell Prize at NIST, put to rest a debate about the nature of quantum reality that had persisted for eight decades<sup>[9](https://www.nist.gov/awards/bell-prize-goes-scientists-who-proved-spooky-quantum-entanglement-real)</sup>.

A review by the Horodecki family of researchers at the University of Gdańsk, published in *Reviews of Modern Physics* in 2009, observed that entanglement, recognized by Einstein, Podolsky, Rosen, and Schrödinger, waited over 70 years to enter laboratories as a new resource "as real as energy"<sup>[10](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.81.865)</sup>.

## What entanglement cannot do

Entangled correlations are stronger than anything classically achievable, yet they cannot be harnessed to make instantaneous, faster-than-light communication possible<sup>[5](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.250401)</sup>. [Gilles Brassard](https://www.edgepedia.org/gilles-brassard) of the [Université de Montréal](https://www.edgepedia.org/universite-de-montreal) and colleagues showed in 2006 a partial answer to why quantum correlations are not maximal among those preserving causality: slightly stronger correlations would result in a world in which communication complexity becomes trivial, meaning distributed computations would become so easy that the notion loses meaning<sup>[5](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.250401)</sup>.

## Entanglement as a resource

The practical turn came with quantum information science. The connection between entanglement and remote, secure cryptographic key generation was discovered in 1991, greatly advancing quantum communication<sup>[6](https://www.nature.com/articles/s41534-025-01072-3)</sup>. [Quantum teleportation](https://www.edgepedia.org/quantum-teleportation), the transfer of an unknown quantum state from one particle to another, was first demonstrated in 1997 by Anton Zeilinger and his colleagues; it is not the only way to transfer quantum information faithfully, since direct physical transmission can also preserve the state, but it transfers quantum information without losing any part of it, at the price of destroying the state in the original particle<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup><sup> • </sup><sup>[18](https://qiskit.qotlabs.org/learning/courses/basics-of-quantum-information/entanglement-in-action/quantum-teleportation)</sup>. A 2023 review in *Nature Reviews Physics* describes teleportation, thirty years after it was proposed, as one of the most important protocols in quantum information, useful for overcoming distance limits in communication and for realizing long-range interactions among qubits in computation<sup>[11](https://www.nature.com/articles/s42254-023-00588-x)</sup>.

**Extending distances.** In 1998 Zeilinger's research group demonstrated entanglement swapping, in which particles from two separate entangled pairs become entangled with each other despite never having been in contact<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup>. Because ordinary optical amplifiers would break entanglement by measuring the light, swapping is the method by which entangled signals can be carried over longer distances in a quantum network than a single fiber span allows<sup>[3](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)</sup>.

**Forms of photonic entanglement.** Polarization entanglement was for decades the workhorse of both foundational tests and applications, but it is limited to two-dimensional, qubit encoding<sup>[6](https://www.nature.com/articles/s41534-025-01072-3)</sup>. In 1989 James Franson (the review names him as Franson) proposed energy-time entanglement, exploiting the unpredictable generation time of a photon pair; a 1999 modification with precise time synchronization gave time-bin entanglement, which enabled large increases in propagation distance and underlies many real-world quantum communication demonstrations<sup>[6](https://www.nature.com/articles/s41534-025-01072-3)</sup>. These forms have been used for entanglement-based quantum key distribution, quantum random number generation, storage on quantum memories, cluster states for one-way quantum computing, and quantum secret sharing, among other tasks<sup>[6](https://www.nature.com/articles/s41534-025-01072-3)</sup>.

**Certification.** Because entanglement is difficult to quantify exactly for most systems, a range of detection and certification methods exists, whose applicability depends on the assumptions made about the states and measurements involved. Certification matters for securing quantum communication, improving sensing sensitivity, and benchmarking quantum computers; a stated goal is device-independent certification, which relies on minimal assumptions<sup>[12](https://www.nature.com/articles/s42254-018-0003-5)</sup>.

## Fragility and decoherence

Entanglement is usually fragile to the environment<sup>[10](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.81.865)</sup>. The formation of entanglement between a system and its environment is a major driving mechanism for decoherence, the disappearance of simple phase relations through environmental interaction<sup>[13](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.042406)</sup>. In spin-based quantum devices, the hyperfine interaction between an electron spin qubit and surrounding nuclear spins remains one of the main sources of decoherence<sup>[14](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.085428)</sup>. Not all entangled states are equally vulnerable: theoretical work distinguishes classes of states that are fragile under decoherence from robust ones that can be disentangled only if decoherence is perfect<sup>[15](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.090501)</sup>.

In quantum computing, entanglement underpins error correction and algorithms that outperform classical counterparts, and achieving high-fidelity entanglement across many qubits remains a central challenge due to decoherence, gate errors, and readout noise<sup>[16](https://www.nature.com/nature-index/topics/l4/quantum-entanglement-in-quantum-computing-systems)</sup>.

## References

1. [The Royal Swedish Academy of Sciences (2022). Advanced information: Nobel Prize in Physics 2022, quoting Schrödinger's 1935 article.](https://www.nobelprize.org/uploads/2026/05/advanced-physicsprize-2022-5.pdf)
2. [All Nobel Prizes, NobelPrize.org: Nobel Prize in Physics 2022.](https://www.nobelprize.org/prizes/lists/all-nobel-prizes/all/?gallery_style=page)
3. [The Nobel Prize in Physics 2022, Popular science background: How entanglement has become a powerful tool.](https://www.nobelprize.org/prizes/physics/2022/popular-information/Using/)
4. [IBM Quantum Learning, Basics of quantum information: Entanglement in action.](https://learning.quantum.ibm.com/course/basics-of-quantum-information/entanglement-in-action)
5. [Brassard, G., Buhrman, H., Linden, N., Méthot, A. A., Tapp, A., Unger, F. (2006). Limit on Nonlocality in Any World in Which Communication Complexity Is Not Trivial. Phys. Rev. Lett. 96, 250401.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.250401)
6. [Xavier, G. B., Larsson, J.-Å., Villoresi, P., Vallone, G., Cabello, A. (2025). Energy-time and time-bin entanglement: past, present and future. npj Quantum Information 11, 129.](https://www.nature.com/articles/s41534-025-01072-3)
7. [IBM Quantum Learning, Utility-scale quantum computing: Bits, gates, and circuits.](https://quantum.cloud.ibm.com/learning/en/courses/utility-scale-quantum-computing/bits-gates-and-circuits)
8. [Erhard, M., Krenn, M., Zeilinger, A. (2020). Advances in high-dimensional quantum entanglement. Nature Reviews Physics 2, 365–381.](https://www.nature.com/articles/s42254-020-0193-5)
9. [NIST (2016). Bell Prize goes to scientists who proved "spooky" quantum entanglement is real.](https://www.nist.gov/awards/bell-prize-goes-scientists-who-proved-spooky-quantum-entanglement-real)
10. [Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K. (2009). Quantum entanglement. Rev. Mod. Phys. 81, 865.](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.81.865)
11. [Hu, X.-M., Guo, Y., Liu, B.-H., Li, C.-F., Guo, G.-C. (2023). Progress in quantum teleportation. Nature Reviews Physics 5, 339–353.](https://www.nature.com/articles/s42254-023-00588-x)
12. [Friis, N., Vitagliano, G., Malik, M., Huber, M. (2019). Entanglement certification from theory to experiment. Nature Reviews Physics 1, 72–87.](https://www.nature.com/articles/s42254-018-0003-5)
13. [Provazza, J., Tempelaar, R. (2022). How system-environment entanglement formation drives quantum decoherence. Phys. Rev. A 106, 042406.](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.042406)
14. [Salamon, T., Płodzień, M., Lewenstein, M., Roszak, K. (2023). Qubit-environment entanglement outside of pure decoherence: Hyperfine interaction. Phys. Rev. B 107, 085428.](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.085428)
15. [Novotný, J., Alber, G., Jex, I. (2011). Entanglement and Decoherence: Fragile and Robust Entanglement. Phys. Rev. Lett. 107, 090501.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.107.090501)
16. [Nature Index, Quantum Entanglement in Quantum Computing Systems.](https://www.nature.com/nature-index/topics/l4/quantum-entanglement-in-quantum-computing-systems)
17. [Entanglement & Correlations - Azure Quantum](https://learn.microsoft.com/en-us/azure/quantum/concepts-entanglement)
18. [Quantum teleportation, IBM Quantum Documentation](https://qiskit.qotlabs.org/learning/courses/basics-of-quantum-information/entanglement-in-action/quantum-teleportation)

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*Topic: Encyclopedia › Physical world and mathematics › Physics › Quantum physics › Quantum mechanics › Quantum phenomena and measurement › Entanglement and nonlocal correlations › Entanglement overview and survey*

*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 15, 2026 · Edited: Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*

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