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| {{merge|Cat state|date=February 2013|discuss=talk: Cat state #Proposed merge}}
| | The author is called Irwin Wunder but it's not the most masucline name out there. Minnesota has usually been his home but his spouse desires them to move. Doing ceramics is what her family and her appreciate. For many years he's been working as a meter reader and it's some thing he truly appreciate.<br><br>Also visit my web site - [http://www.videokeren.com/user/FJWW http://www.videokeren.com/] |
| In [[physics]], in the area of [[quantum information theory]], a '''Greenberger–Horne–Zeilinger state''' is a certain type of [[quantum entanglement|entangled]] [[quantum state]] which involves at least three subsystems (particles). It was first studied by D. Greenberger, M.A. Horne and [[Anton Zeilinger]] in 1989.<ref>{{citation |author=Daniel M. Greenberger, Michael A. Horne, Anton Zeilinger |year=2007 |title=Going beyond Bell's Theorem |arxiv=0712.0921|bibcode = 2007arXiv0712.0921G }}</ref> They have noticed the extremely non-classical properties of the state.
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| ==Definition==
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| The '''GHZ state''' is an [[quantum entanglement|entangled]] [[quantum state]] of {{math|''M'' > 2}} subsystems. In the case of each of the subsystems being two-dimensional, that is for [[qubit]]s, it reads
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| :<math>|\mathrm{GHZ}\rangle = \frac{|0\rangle^{\otimes M} + |1\rangle^{\otimes M}}{\sqrt{2}}.</math>
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| In simple words it is a quantum superposition of all subsystems being in state 0 with all of them being in state 1 (states 0 and 1 of a single subsystem are fully distinguishable).
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| The simplest one is the 3-qubit GHZ state:
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| <math>|\mathrm{GHZ}\rangle = \frac{|000\rangle + |111\rangle}{\sqrt{2}}.</math> | |
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| ==Properties==
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| There is no standard measure of multi-partite entanglement because different types of multi-partite entanglement exist which are not mutually convertible. Nonetheless, many measures define the GHZ to be [[Maximally entangled state|maximally entangled]].
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| Another important property of the GHZ state is that when we [[partial trace|trace]] over one of the three systems
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| we get
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| :<math>\mathrm{Tr}_3\big((|000\rangle + |111\rangle)(\langle 000|+\langle 111|) \big) = |00\rangle \langle 00| + |11\rangle \langle 11|</math> | |
| which is an unentangled [[mixed state (physics)|mixed state]]. It has certain two-particle (qubit) correlations, but these are [[covariation|of a classical nature]].
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| On the other hand, if we were to measure one of the subsystems, in such a way that the measurement distinguishes between the states 0 and 1, we will leave behind either <math>|00\rangle</math> or <math>|11\rangle</math> which are unentangled pure states. This is unlike the [[W state]] which leaves bipartite entanglements even when we measure one of its subsystems.
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| The GHZ state leads to striking non-classical correlations (1989). Particles prepared in this state lead to a version of [[Bell's theorem]], which shows the internal inconsistency of the notion of elements-of-reality introduced in the famous [[Einstein–Podolsky–Rosen paradox|Einstein–Podolsky–Rosen]] paper. The first laboratory observation of GHZ correlations was by the group of [[Anton Zeilinger]] (1998). Many, more accurate observations followed. The correlations can be utilized in some [[quantum information]] tasks. These include multipartner [[quantum cryptography]] (1998) and [[communication complexity]] tasks (1997, 2004).
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| ==See also==
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| * [[Bell's theorem]]
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| * [[Bell state]]
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| * [[GHZ experiment]]
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| * [[Local hidden variable theory]]
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| * [[Quantum entanglement]]
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| * [[Qubit]]
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| * [[Measurement in quantum mechanics]]
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| ==References==
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| <references/>
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| {{DEFAULTSORT:Greenberger-Horne-Zeilinger state}}
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| [[Category:Quantum information theory]]
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| {{Physics-stub}}
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| [[de:GHZ-Experiment|Greenberger-Horne-Zeilinger]]
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| [[ja:Greenberger-Horne-Zeilinger 状態]]
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The author is called Irwin Wunder but it's not the most masucline name out there. Minnesota has usually been his home but his spouse desires them to move. Doing ceramics is what her family and her appreciate. For many years he's been working as a meter reader and it's some thing he truly appreciate.
Also visit my web site - http://www.videokeren.com/