Nathaniel: Created page with "{{Function |name=Bell |desc=Produces a Bell state |rel=MaxEntangled |cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]..."

2014-09-23T17:16:38Z

Created page with "{{Function |name=Bell |desc=Produces a Bell state |rel=MaxEntangled |cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]..."

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{{Function
|name=Bell
|desc=Produces a Bell state
|rel=[[MaxEntangled]]
|cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]]
|upd=September 23, 2014
|v=0.50}}
<tt>'''Bell'''</tt> is a [[List of functions|function]] that returns one of the four Bell states in 2-qubit space:
<center><math>\displaystyle\begin{align*}|\phi_0\rangle = \frac{1}{\sqrt{2}}(|0\rangle\otimes|0\rangle + |1\rangle\otimes|1\rangle) & & & & |\phi_2\rangle = \frac{1}{\sqrt{2}}(|0\rangle\otimes|1\rangle + |1\rangle\otimes|0\rangle) \\ |\phi_1\rangle = \frac{1}{\sqrt{2}}(|0\rangle\otimes|0\rangle - |1\rangle\otimes|1\rangle) & & & & |\phi_3\rangle = \frac{1}{\sqrt{2}}(|0\rangle\otimes|1\rangle - |1\rangle\otimes|0\rangle) \\\end{align*}</math></center>

==Syntax==
* <tt>PHI = Bell()</tt>
* <tt>PHI = Bell(IND)</tt>
* <tt>PHI = Bell(IND,SP)</tt>
* <tt>PHI = Bell(IND,SP,NRML)</tt>

==Argument descriptions==
* <tt>IND</tt> (optional, default 0): The index of the Bell state (i.e., the subscript, from 0 to 3, of the Bell state that you would like, as indicated above).
* <tt>SP</tt> (optional, default 0): A flag (either 1 or 0) indicating that <tt>PHI</tt> should or should not be sparse.
* <tt>NRML</tt> (optional, default 1): A flag (either 1 or 0) indicating that <tt>PHI</tt> should or should not be scaled to have Euclidean norm 1. If <tt>NRML=0</tt> then each entry of <tt>PHI</tt> is 0 or 1, so it has norm $\sqrt{2}$.

==Examples==
The following code generates a matrix whose columns are the four different Bell states:
<syntaxhighlight>
>> [Bell(0),Bell(1),Bell(2),Bell(3)]

ans =

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

{{SourceCode|name=Bell}}

Bell - Revision history

Nathaniel: Created page with "{{Function |name=Bell |desc=Produces a Bell state |rel=MaxEntangled |cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]..."