|Produces a Breuer state of even dimension ≥ 2|
|Other toolboxes required||none|
|Function category||Special states, vectors, and operators|
BreuerState is a function that produces a two-qudit "Breuer state" (i.e., the state defined in ). These states are of interest because they are bound entangled. The output of this function is sparse.
- BREUER_STATE = BreuerState(DIM,LAMBDA)
- DIM: The local dimension (must be ≥ 2 and even).
- LAMBDA: The weight of the singlet component in the state (see  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)).
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
Click on "expand" to the right to view the MATLAB source code for this function.
- H.-P. Breuer. Optimal entanglement criterion for mixed quantum states. Phys. Rev. Lett., 97:080501, 2006. E-print: arXiv:quant-ph/0605036