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