Nathaniel: Added link to Wikipedia

2014-12-20T04:07:07Z

Added link to Wikipedia

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	\|cat=[[List of functions#Special_states,_vectors,_and_operators\|Special states, vectors, and operators]]		\|cat=[[List of functions#Special_states,_vectors,_and_operators\|Special states, vectors, and operators]]
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	<tt>'''GHZState'''</tt> is a [[List of functions\|function]] that returns a GHZ state on a given number of qubits (or qudits). For example, the usual $3$-qubit GHZ state is $\frac{1}{\sqrt{2}}(\|000\rangle + \|111\rangle)$. More generally, the GHZ state on $q$ qudits with local dimension $d$ is $\frac{1}{\sqrt{d}}\sum_{j=0}^{d-1} \|j\rangle^{\otimes q}$. The output of this function is a sparse vector.		<tt>'''GHZState'''</tt> is a [[List of functions\|function]] that returns a [http://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state GHZ state] on a given number of qubits (or qudits). For example, the usual $3$-qubit GHZ state is $\frac{1}{\sqrt{2}}(\|000\rangle + \|111\rangle)$. More generally, the GHZ state on $q$ qudits with local dimension $d$ is $\frac{1}{\sqrt{d}}\sum_{j=0}^{d-1} \|j\rangle^{\otimes q}$. The output of this function is a sparse vector.

	==Syntax==		==Syntax==

Nathaniel: Created page with "{{Function |name=GHZState |desc=Generates a (generalized) GHZ state |rel=DickeState
MaxEntangled
WState |cat=List of functions#Special_states,_vectors,..."

2014-12-20T04:06:35Z

Created page with "{{Function |name=GHZState |desc=Generates a (generalized) GHZ state |rel=DickeState<br />MaxEntangled<br />WState |cat=List of functions#Special_states,_vectors,..."

New page

{{Function
|name=GHZState
|desc=Generates a (generalized) GHZ state
|rel=[[DickeState]]<br />[[MaxEntangled]]<br />[[WState]]
|cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]]
|upd=December 15, 2014}}
<tt>'''GHZState'''</tt> is a [[List of functions|function]] that returns a GHZ state on a given number of qubits (or qudits). For example, the usual $3$-qubit GHZ state is $\frac{1}{\sqrt{2}}(|000\rangle + |111\rangle)$. More generally, the GHZ state on $q$ qudits with local dimension $d$ is $\frac{1}{\sqrt{d}}\sum_{j=0}^{d-1} |j\rangle^{\otimes q}$. The output of this function is a sparse vector.

==Syntax==
* <tt>GHZ_STATE = GHZState(DIM,Q)</tt>
* <tt>GHZ_STATE = GHZState(DIM,Q,COEFF)</tt>

==Argument descriptions==
* <tt>DIM</tt>: The local dimension.
* <tt>Q</tt>: The number of qubits (or qudits, if <tt>DIM > 2</tt>).
* <tt>COEFF</tt> (optional, default <tt>[1,1,...,1]/sqrt(DIM)</tt>): A vector whose $j$-th entry is the coefficient of the term $|j-1\rangle^{\otimes q}$ in the generalized GHZ state.

==Examples==
===3-qubit GHZ state===
The following code generates the usual 3-qubit GHZ state:
<syntaxhighlight>
>> full(GHZState(2,3))

ans =

0.7071
0
0
0
0
0
0
0.7071
</syntaxhighlight>

===A 7-qudit GHZ state===
The following code generates the following GHZ state living in $(\mathbb{C}^4)^{\otimes 7}$:
: <math>\frac{1}{\sqrt{30}}\big( |0000000\rangle + 2|1111111\rangle + 3|2222222\rangle + 4|3333333\rangle \big).</math>
<syntaxhighlight>
>> GHZState(4,7,[1,2,3,4]/sqrt(30))

ans =

(1,1) 0.1826
(5462,1) 0.3651
(10923,1) 0.5477
(16384,1) 0.7303
</syntaxhighlight>

===A very large GHZ state===
This script has no trouble creating GHZ states on very large numbers of qudits. The following code generates the GHZ state in $(\mathbb{C}^3)^{\otimes 30}$:
<syntaxhighlight>
>> GHZState(3,30)

ans =

(1,1) 0.5774
(102945566047325,1) 0.5774
(205891132094649,1) 0.5774
</syntaxhighlight>

{{SourceCode|name=GHZState}}

GHZState - Revision history

Nathaniel: Added link to Wikipedia

Nathaniel: Created page with "{{Function |name=GHZState |desc=Generates a (generalized) GHZ state |rel=DickeStateMaxEntangledWState |cat=List of functions#Special_states,_vectors,..."

Nathaniel: Created page with "{{Function |name=GHZState |desc=Generates a (generalized) GHZ state |rel=DickeState
MaxEntangled
WState |cat=List of functions#Special_states,_vectors,..."