W state

The W state is an entangled quantum state of three qubits which in the bra-ket notation has the following shape

|\mathrm {W} \rangle ={\frac {1}{\sqrt {3}}}(|001\rangle +|010\rangle +|100\rangle )

and which is remarkable for representing a specific type of multipartite entanglement and for occurring in several applications in quantum information theory. Particles prepared in this state reproduce the properties of Bell's theorem, which states that no classical theory of local hidden variables can produce the predictions of quantum mechanics. The state is named after Wolfgang Dür,^[1] who first reported the state together with Guifré Vidal, and Ignacio Cirac in 2002.^[2]

^ Cabello, Adán (February 5, 2002). "Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states". Physical Review A. 65 (3): 032108. arXiv:quant-ph/0107146. Bibcode:2002PhRvA..65c2108C. doi:10.1103/PhysRevA.65.032108. ISSN 1050-2947. S2CID 55659305.
^ W. Dür; G. Vidal & J. I. Cirac (2000). "Three qubits can be entangled in two inequivalent ways". Phys. Rev. A. 62 (6): 062314. arXiv:quant-ph/0005115. Bibcode:2000PhRvA..62f2314D. doi:10.1103/PhysRevA.62.062314. S2CID 16636159.

[1] Cabello, Adán (February 5, 2002). "Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states". Physical Review A. 65 (3): 032108. arXiv:quant-ph/0107146. Bibcode:2002PhRvA..65c2108C. doi:10.1103/PhysRevA.65.032108. ISSN 1050-2947. S2CID 55659305.

[Duer2000-2] W. Dür; G. Vidal & J. I. Cirac (2000). "Three qubits can be entangled in two inequivalent ways". Phys. Rev. A. 62 (6): 062314. arXiv:quant-ph/0005115. Bibcode:2000PhRvA..62f2314D. doi:10.1103/PhysRevA.62.062314. S2CID 16636159.

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