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| The '''W state''' is an [[quantum entanglement|entangled]] [[quantum state]] of three [[qubits]] which has the following shape
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| : <math>|W\rangle = \frac{1}{\sqrt{3}}(|001\rangle + |010\rangle + |100\rangle)</math>
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| and which is remarkable for representing a specific type of [[multipartite entanglement]] and for occurring in several applications in [[quantum information theory]]. | |
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| ==Properties==
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| The W state is the representative of one of the two non-biseparable<ref>A pure state <math>|\psi\rangle</math> of <math>N</math> parties is called ''biseparable'', if one can find a partition of the parties in two disjoint subsets <math>A</math> and <math>B</math> with <math>A\cup B=\{1,...,N\}</math> such that <math>|\psi\rangle = |\phi\rangle_A\otimes|\gamma\rangle_B</math>, i.e. <math>|\psi\rangle</math> is a [[product state]] with respect to he partition <math>A|B</math>.</ref> classes of three-qubit states (the other being the [[Greenberger-Horne-Zeilinger state|GHZ state]]) which cannot be transformed (not even probabilistically) into each other by [[LOCC|local quantum operations]].<ref name="Duer2000">{{cite journal|author=W. Dür, G. Vidal, and J.I. Cirac|title=Three qubits can be entangled in two inequivalent ways|journal=Phys. Rev. A|volume=62|pages=062314|year=2000| doi=10.1103/PhysRevA.62.062314|arxiv=quant-ph/0005115|bibcode = 2000PhRvA..62f2314D }}</ref> Thus <math>|W\rangle</math> and <math>|GHZ\rangle</math> represent two very different kinds of tripartite entanglement.
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| This difference is, for example, illustrated by the following interesting property of the W state: if one of the three qubits is lost, the state of the remaining 2-qubit system is still entangled. This robustness of W-type entanglement contrasts strongly with the [[Greenberger-Horne-Zeilinger state]] which is fully separable after loss of one qubit.
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| The states in the W class can be distinguished from all other three-qubit states by means of [[Multipartite entanglement#Multipartite entanglement measures for pure states|multipartite entanglement measures]]. In particular, W states have non-zero entanglement across any bipartition<ref>A bipartition of the three qubits <math>1,2,3</math> is any grouping <math>(12) 3, 1 (23)</math> and <math>(13) 2</math> in which two qubits are considered to belong to the same party. The three qubit state can then be considered as a state on <math>\mathbb{C}^4\otimes \mathbb{C}^2</math> and studied with bipartite entanglement measures.</ref> while the 3-tangle vanishes, which is also non-zero for GHZ-type states.<ref name="Duer2000" />
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| == Generalization ==
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| The notion of W state has been generalized for <math>n</math> qubits<ref name="Duer2000" /> and then refers to the quantum superpostion with equal expansion coefficients of all possible pure states in which exactly one of the qubits in an "excited state" <math> |1\rangle</math>, while all other ones are in the "ground state" <math> |0\rangle</math>
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| : <math>|W\rangle = \frac{1}{\sqrt{N}}(|100...0\rangle + |010...0\rangle + ... + |00...01\rangle)</math>
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| Both the robustness against particle loss and the LOCC-inequivalence with the (generalized) GHZ state also hold for the <math>n</math>-qubit W state.
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| == Applications ==
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| In systems in which a single qubit is stored in an ensemble of many two level systems the logical "1" is often represented by the W state while the logical "0" is represented by the state <math>|00...0\rangle</math>. Here the W state's robustness against particle loss is a very beneficial property ensuring good storage properties of these ensemble based quantum memories.<ref>{{cite journal|title=Quantum memory for photons: Dark-state polaritons|author=M. Fleischhauer and M. D. Lukin|volume=Phys. Rev. A|volume=65|pages=022314|year=2002|doi=10.1103/PhysRevA.65.022314|arxiv=quant-ph/0106066|bibcode = 2002PhRvA..65b2314F }}</ref>
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| == References ==
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| <references />
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| {{DEFAULTSORT:W State}}
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| [[Category:Quantum information theory]]
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Hi there, I am Alyson Pomerleau and I think it seems fairly good when you say it. I've always cherished residing in Mississippi. Invoicing is what I do. To climb is some thing she would by no means give up.
Also visit my blog - online reader (165.132.39.93)