Optimal stopping - Revision history

en>Magioladitis: clean up using AWB (10058)

2014-03-28T06:28:29Z

clean up using AWB (10058)

← Older revision		Revision as of 08:28, 28 March 2014
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	~~Hi there. Let me begin~~ by ~~introducing~~ the ~~writer, her name is~~ Myrtle ~~Cleary~~. ~~His wife doesn~~'~~t like it the way he does~~ but what ~~he really~~ likes ~~performing~~ is to ~~do aerobics and he's been doing~~ it ~~for quite a while~~. ~~Puerto Rico~~ is where he and ~~his spouse~~ live. Hiring is ~~her day occupation now and she will not alter it whenever soon~~.<br><br>~~My website;~~ [http://~~www.sddch~~.~~org~~/~~?document_srl=345265 http:~~//~~www.sddch.org~~/~~?document_srl=345265~~]		She is known by the title of Myrtle Shryock. It's not a typical factor but what she likes doing is base jumping and now she is attempting to make money with it. South Dakota is where me and my husband live. Hiring is my profession.<br><br>Have a look at my web blog - [http://youulike.com/blogs/114396/390615/items-to-know-when-confronted-wi home std test]

en>Dorassohn: Ref. added

2014-02-05T09:56:05Z

Ref. added

← Older revision		Revision as of 11:56, 5 February 2014
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	~~In [[quantum information theory]],~~ the ~~'''reduction criterion''' is a necessary condition a [[Mixed state (physics)\|mixed state]] must satisfy in order for it to be [[separable state\|separable]]. In other words~~, ~~the reduction criterion is a ''separability criterion''. It was fist proved in <ref name="HH99" />~~		Hi there. Let me begin by introducing the writer, her name is Myrtle Cleary. His wife doesn't like it the way he does but what he really likes performing is to do aerobics and he's been doing it for quite a while. Puerto Rico is where he and his spouse live. Hiring is her day occupation now and she will not alter it whenever soon.<br><br>My website; [http://www.sddch.org/?document_srl=345265 http://www.sddch.org/?document_srl=345265]
	~~and independently formulated in.<ref~~ name~~="Cerf99" /> Violation of the reduction criterion~~ is ~~closely related to the [[entanglement distillation\|distillability]] of the state in question~~.~~<ref name="HH99" />~~

	~~==Details==~~
	~~Let ''H''<sub>1</sub> and ''H''<sub>2</sub> be Hilbert spaces of finite dimensions ''n'' and ''m'' respectively. ''L''('~~'~~H<sub>i</sub>'') will denote the space of linear operators acting on ''H<sub>i</sub>''. Consider a bipartite quantum system whose state space is the tensor product~~

	~~:<math> H = H_1 \otimes H_2.</math>~~

	~~An (un-normalized) mixed state ''ρ'' is a positive linear operator (density matrix) acting on ''H''.~~

	~~A linear map Φ: ''L''(''H''<sub>2</sub>) → ''L''(''H''<sub>1</sub>) is said to be positive if~~ it ~~preserves~~ the ~~cone of positive elements, i.e. ''A''~~ is ~~positive implied ''Φ''(''A'') is also.~~

	~~From the one-~~to~~-one correspondence between positive maps~~ and ~~[[entanglement witness]]es, we have that a state~~ '~~'ρ'' is entangled if and only if there exists a positive map ''Φ'' such that~~

	~~:<math>(I \otimes \Phi)(\rho)</math>~~

	~~is not positive. Therefore, if ''ρ'' is separable, then~~ for ~~all positive map Φ,~~

	~~:<math>(I \otimes \Phi)(\rho) \geq 0.</math>~~

	~~Thus every positive, but not [[completely positive map\|completely positive]], map Φ gives rise to~~ a ~~necessary condition for separability in this way~~. ~~The reduction criterion~~ is ~~a particular example of this~~.

	~~Suppose ''H''<sub>1</sub> = ''H''<sub>2</sub>. Define the positive map Φ: ''L''(''H''<sub>2</sub>) → ''L''(''H''<sub>1</sub>) by~~

	~~:<math>\Phi(A) = \operatorname{Tr}A - A.</math>~~

	It is ~~known that Φ is positive but~~ not ~~completely positive~~. ~~So a mixed state ''ρ'' being separable implies~~

	:<~~math~~>~~(I \otimes \Phi) (\rho) \geq 0.~~<~~/math~~>

	~~Direct calculation shows that the above expression is the same as~~

	:~~<math>I \otimes \rho_1 - \rho \geq 0<~~/~~math>~~

	~~where ''ρ''<sub>1</sub> is the [[partial trace]] of ''ρ'' with respect to the second system. The dual relation~~

	~~:<math>\rho_2 \otimes I - \rho \geq 0<~~/~~math>~~

	~~is obtained in the analogous fashion. The reduction criterion consists of the above two inequalities. The reduction criterion is~~

	~~==References==~~
	~~<references>~~
	~~<ref name="HH99">{{cite journal\|journal=Phys. Rev. A\|volume='''59'''\|pages= 4206\|year=1999\|author=M~~. ~~Horodecki and P~~. ~~Horodecki\|title=Reduction criterion of separability and limits for a class of distillation protocols\|doi=10.1103~~/~~PhysRevA.59.4206\|arxiv~~=~~quant-ph~~/~~9708015}}<~~/~~ref>~~
	~~<ref name="Cerf99">{{cite journal\|journal=Phys. Rev. A\|volume='''60'''\|pages= 898\|year=1999\|author=N~~. ~~Cerf ''et al.''\|title=Reduction criterion for separability\|doi=10~~.~~1103~~/~~PhysRevA.60.898\|arxiv~~=~~quant-ph/9710001}}</ref>~~
	~~</references>~~

	~~{{DEFAULTSORT:Reduction Criterion}}~~
	~~[[Category:Quantum information science]~~]

en>ChrisGualtieri: General Fixes using AWB

2013-10-24T00:06:05Z

General Fixes using AWB

← Older revision		Revision as of 02:06, 24 October 2013
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	~~She~~ is ~~recognized by~~ the name of ~~Myrtle Shryock~~. ~~My working day job~~ is a ~~librarian~~. ~~Doing ceramics~~ is ~~what adore doing~~. ~~California~~ is ~~exactly where her std testing at home~~ - [~~http~~://~~www~~.~~animecontent~~.~~com~~/~~blog~~/~~349119 Full Posting],~~ is but ~~she requirements~~ to ~~transfer because~~ of ~~her family members~~.		In [[quantum information theory]], the '''reduction criterion''' is a necessary condition a [[Mixed state (physics)\|mixed state]] must satisfy in order for it to be [[separable state\|separable]]. In other words, the reduction criterion is a ''separability criterion''. It was fist proved in <ref name="HH99" />
			and independently formulated in.<ref name="Cerf99" /> Violation of the reduction criterion is closely related to the [[entanglement distillation\|distillability]] of the state in question.<ref name="HH99" />

			==Details==
			Let ''H''<sub>1</sub> and ''H''<sub>2</sub> be Hilbert spaces of finite dimensions ''n'' and ''m'' respectively. ''L''(''H<sub>i</sub>'') will denote the space of linear operators acting on ''H<sub>i</sub>''. Consider a bipartite quantum system whose state space is the tensor product

			:<math> H = H_1 \otimes H_2.</math>

			An (un-normalized) mixed state ''ρ'' is a positive linear operator (density matrix) acting on ''H''.

			A linear map Φ: ''L''(''H''<sub>2</sub>) → ''L''(''H''<sub>1</sub>) is said to be positive if it preserves the cone of positive elements, i.e. ''A'' is positive implied ''Φ''(''A'') is also.

			From the one-to-one correspondence between positive maps and [[entanglement witness]]es, we have that a state ''ρ'' is entangled if and only if there exists a positive map ''Φ'' such that

			:<math>(I \otimes \Phi)(\rho)</math>

			is not positive. Therefore, if ''ρ'' is separable, then for all positive map Φ,

			:<math>(I \otimes \Phi)(\rho) \geq 0.</math>

			Thus every positive, but not [[completely positive map\|completely positive]], map Φ gives rise to a necessary condition for separability in this way. The reduction criterion is a particular example of this.

			Suppose ''H''<sub>1</sub> = ''H''<sub>2</sub>. Define the positive map Φ: ''L''(''H''<sub>2</sub>) → ''L''(''H''<sub>1</sub>) by

			:<math>\Phi(A) = \operatorname{Tr}A - A.</math>

			It is known that Φ is positive but not completely positive. So a mixed state ''ρ'' being separable implies

			:<math>(I \otimes \Phi) (\rho) \geq 0.</math>

			Direct calculation shows that the above expression is the same as

			:<math>I \otimes \rho_1 - \rho \geq 0</math>

			where ''ρ''<sub>1</sub> is the [[partial trace]] of ''ρ'' with respect to the second system. The dual relation

			:<math>\rho_2 \otimes I - \rho \geq 0</math>

			is obtained in the analogous fashion. The reduction criterion consists of the above two inequalities. The reduction criterion is

			==References==
			<references>
			<ref name="HH99">{{cite journal\|journal=Phys. Rev. A\|volume='''59'''\|pages= 4206\|year=1999\|author=M. Horodecki and P. Horodecki\|title=Reduction criterion of separability and limits for a class of distillation protocols\|doi=10.1103/PhysRevA.59.4206\|arxiv=quant-ph/9708015}}</ref>
			<ref name="Cerf99">{{cite journal\|journal=Phys. Rev. A\|volume='''60'''\|pages= 898\|year=1999\|author=N. Cerf ''et al.''\|title=Reduction criterion for separability\|doi=10.1103/PhysRevA.60.898\|arxiv=quant-ph/9710001}}</ref>
			</references>

			{{DEFAULTSORT:Reduction Criterion}}
			[[Category:Quantum information science]]

en>Yutiannie: /* Option trading */

2012-06-02T19:44:42Z

Option trading

New page

She is recognized by the name of Myrtle Shryock. My working day job is a librarian. Doing ceramics is what adore doing. California is exactly where her std testing at home - [http://www.animecontent.com/blog/349119 Full Posting], is but she requirements to transfer because of her family members.