Keratometer - Revision history

en>Marc Hens at 15:39, 15 August 2014

2014-08-15T15:39:12Z

← Older revision		Revision as of 17:39, 15 August 2014
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	~~The '''W state''' is an [[quantum entanglement\|entangled]] [[quantum state]] of three [[qubits]] which has the following shape~~		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.<br><br>Also visit my blog - online reader ([http://165.132.39.93/xe/visitors/372912 165.132.39.93])
	~~: <math>\|W\rangle = \frac{1}{\sqrt{3}}(\|001\rangle + \|010\rangle + \|100\rangle)</math>~~
	and ~~which is remarkable for representing a specific type of [[multipartite entanglement]] and for occurring in several applications in [[quantum information theory]]~~.

	~~==Properties==~~
	~~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.

	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.~~

	~~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" />~~

	~~== Generalization ==~~

	~~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>~~
	~~: <math>\|W\rangle = \frac{1}{\sqrt{N}}(\|100~~...~~0\rangle + \|010...0\rangle + ... + \|00...01\rangle~~)~~</math>~~
	~~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.~~

	~~== Applications ==~~
	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>

	~~== References ==~~
	~~<references />~~

	~~{{DEFAULTSORT:W State}}~~
	~~[[Category:Quantum information theory]]~~

en>BDD: removing deleted portal

2013-11-18T18:14:27Z

removing deleted portal

← Older revision		Revision as of 20:14, 18 November 2013
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	~~Greetings~~. The ~~writer~~'s title is ~~Phebe and she feels comfortable when individuals use~~ the ~~full title~~. ~~One~~ of the ~~very very best things~~ in the ~~world~~ for ~~him~~ is to ~~gather badges but he is struggling~~ to ~~discover time for it~~. ~~Managing people is what I do~~ and the ~~wage~~ has been ~~really fulfilling~~. ~~Puerto Rico~~ is ~~where he and his wife reside~~.<br><br>~~Feel free to visit my site :: [http~~://~~www~~.~~innovec~~.~~com~~/~~node~~/~~3171 std testing at home~~]		The '''W state''' is an [[quantum entanglement\|entangled]] [[quantum state]] of three [[qubits]] which has the following shape
			: <math>\|W\rangle = \frac{1}{\sqrt{3}}(\|001\rangle + \|010\rangle + \|100\rangle)</math>
			and which is remarkable for representing a specific type of [[multipartite entanglement]] and for occurring in several applications in [[quantum information theory]].

			==Properties==
			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.

			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.

			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" />

			== Generalization ==

			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>
			: <math>\|W\rangle = \frac{1}{\sqrt{N}}(\|100...0\rangle + \|010...0\rangle + ... + \|00...01\rangle)</math>
			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.

			== Applications ==
			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>

			== References ==
			<references />

			{{DEFAULTSORT:W State}}
			[[Category:Quantum information theory]]

en>Calmer Waters: Undid revision 502813276 by 67.40.236.163 (talk) unexplained removal on content

2012-07-17T16:08:47Z

Undid revision 502813276 by 67.40.236.163 (talk) unexplained removal on content

New page

Greetings. The writer's title is Phebe and she feels comfortable when individuals use the full title. One of the very very best things in the world for him is to gather badges but he is struggling to discover time for it. Managing people is what I do and the wage has been really fulfilling. Puerto Rico is where he and his wife reside.<br><br>Feel free to visit my site :: [http://www.innovec.com/node/3171 std testing at home]