Three qubits can be entangled in two inequivalent ways
Open accessAbstract
Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say that two states have the same kind of entanglement if both of them can be obtained from the other by means of local operations and classical communication (LOCC) with nonzero probability. When applied to pure states of a three-qubit system, this approach reveals the existence of two inequivalent kinds of genuine tripartite entanglement, for which the Greenberger-Horne-Zeilinger state and a W state appear as remarkable representatives. In particular, we show that the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. We generalize our results both to the case of higher-dimensional subsystems and also to more than three subsystems, for all of which we show that, typically, two randomly chosen pure states cannot be converted into each other by means of LOCC, not even with a small probability of success.
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W-states are a class of maximally multipartite entangled states that can be generalized to N qubits.
“One possible class of maximally multipartite entangled states is made up of the so-called W-states.First introduced as coherent and balanced superposition of three qubit states [81] they can be readily generalized to N qubits.”
From Integrated photonic quantum walks (2020) · cites this paper as [81]
The section “State W in multiqubit systems” defines an N-qubit generalization as a balanced, symmetric superposition. The Introduction and Summary and Conclusions describe the three-qubit W state as maximally robust to the loss of a qubit, not as unqualifiedly maximally multipartite entangled; the Introduction notes that GHZ can be regarded as maximally entangled in several respects. Page numbers are unavailable in our copy. (LLM, conf=0.86)
Experimental — accuracy not yet measuredTo restore coherent effects with single photons, single photons need to be produced in W-states.
“We show that single photons need to be produced in W-states which lead to vanishing mean amplitude but nonzero correlations between the inputs at different ports. Such correlations restore coherent effects with single photons.”
This is no longer true in multipartite systems, where inequivalent kinds of multipartite entanglement exist.
“This is no longer true in multipartite systems - where inequivalent kinds of multipartite entanglement exist [70].”
From Measures and dynamics of entangled states (2005) · cites this paper as [70]
GHZ and W states contain fundamentally different correlations, such that none can be created from the other by LOCC alone.
“Both states contain fundamentally different correlations, such that none of the two can be created from the other one by LOCC alone [70].”
From Measures and dynamics of entangled states (2005) · cites this paper as [70]
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- Authors
- Dür, W., Vidal, G., & Cirac, J. I.
- Affiliations
- Universität Innsbruck (AT)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2000-11-14
- Volume
- 62
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1974928788
- Cited by
- 3,384
- References
- 15
- Citations by year
- 2026: 105 · 2025: 191 · 2024: 164 · 2023: 194 · 2022: 127 · 2021: 120 · 2020: 156 · 2019: 149 · 2018: 119 · 2017: 109 · 2016: 147 · 2015: 130 · 2014: 160 · 2013: 167 · 2012: 139
- FWCI
- 52.05
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- European Science Foundation
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- three-qubit entanglement, genuine tripartite entanglement, entanglement classification, GHZ states, W state, bipartite entanglement, random pure states, multipartite entanglement
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