# BreuerState

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 Other toolboxes required BreuerState Produces a Breuer state of even dimension ≥ 2 none ChessboardState 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 on "expand" to the right to view the MATLAB source code for this function.

## References

1. H.-P. Breuer. Optimal entanglement criterion for mixed quantum states. Phys. Rev. Lett., 97:080501, 2006. E-print: arXiv:quant-ph/0605036