# BreuerState

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BreuerState | |

Produces a Breuer state of even dimension ≥ 2 | |

Other toolboxes required | none |
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Related functions | ChessboardState |

Function category | Special states, vectors, and operators |

` BreuerState` is a function that produces a two-qudit "Breuer state" (i.e., the state defined in

^{[1]}). These states are of interest because they are bound entangled. The output of this function is sparse.

## Syntax

`BREUER_STATE = BreuerState(DIM,LAMBDA)`

## Argument descriptions

`DIM`: The local dimension (must be ≥ 2 and even).`LAMBDA`: The weight of the singlet component in the state (see^{[1]}for details). A positive real number between 0 and 1. The state will be separable if and only if`LAMBDA = 0`and it will have positive partial transpose if and only if`LAMBDA <= 1/(DIM + 2)`).

## 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):

```
>> 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
```

## Source code

Click here to view this function's source code on github.

## References

- ↑
^{1.0}^{1.1}H.-P. Breuer. Optimal entanglement criterion for mixed quantum states.*Phys. Rev. Lett.*, 97:080501, 2006. E-print: arXiv:quant-ph/0605036