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Created page with "{{Function |name=BreuerState |desc=Produces a Breuer state of even dimension ≥ 2 |rel=ChessboardState |cat=List of functions#Special_states,_vectors,_and_operators|Sp..."

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{{Function
|name=BreuerState
|desc=Produces a Breuer state of even dimension ≥ 2
|rel=[[ChessboardState]]
|cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]]
|upd=December 15, 2014}}
<tt>'''BreuerState'''</tt> is a [[List of functions|function]] that produces a two-qudit "Breuer state" (i.e., the state defined in <ref name="B06">H.-P. Breuer. Optimal entanglement criterion for mixed quantum states. ''Phys. Rev. Lett.'', 97:080501, 2006. E-print: [http://arxiv.org/abs/quant-ph/0605036 arXiv:quant-ph/0605036]</ref>). These states are of interest because they are bound entangled. The output of this function is sparse.

==Syntax==
* <tt>BREUER_STATE = BreuerState(DIM,LAMBDA)</tt>

==Argument descriptions==
* <tt>DIM</tt>: The local dimension (must be ≥ 2 and even).
* <tt>LAMBDA</tt>: The weight of the singlet component in the state (see <ref name="B06"></ref> for details). A positive real number between 0 and 1. The state will be separable if and only if <tt>LAMBDA = 0</tt> and it will have positive partial transpose if and only if <tt>LAMBDA <= 1/(DIM + 2)</tt>).

==Examples==
===A 4 ⊗ 4 bound entangled state===
The following code generates a bound entangled Breuer state in $M_4 \otimes M_4$ and then verifies that has positive partial transpose and is entangled (and is thus bound entangled):
<syntaxhighlight>
>> rho = full(BreuerState(4,0.1));
>> IsPPT(rho)

ans =

1

>> IsSeparable(rho)
Determined to be entangled by not having a 2-copy PPT symmetric extension. Reference:
A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri. A complete family of separability criteria. Phys. Rev. A, 69:022308, 2004.

ans =

0
</syntaxhighlight>

{{SourceCode|name=BreuerState}}

==References==
<references />

BreuerState - Revision history

Nathaniel: Created page with "{{Function |name=BreuerState |desc=Produces a Breuer state of even dimension ≥ 2 |rel=ChessboardState |cat=List of functions#Special_states,_vectors,_and_operators|Sp..."