Difference between revisions of "SymmetricInnerExtension"
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|desc=Determines whether or not an operator has a symmetric inner extension | |desc=Determines whether or not an operator has a symmetric inner extension | ||
| − | |req=[http://cvxr.com/cvx/ cvx] | + | |req=[http://cvxr.com/cvx/ cvx] |
| − | | | + | |rel=[[IsPPT]]<br />[[IsSeparable]]<br />[[SymmetricExtension]]<br />[[SymmetricProjection]] |
| + | |cat=[[List of functions#Entanglement_and_separability|Entanglement and separability]] | ||
|upd=September 17, 2013 | |upd=September 17, 2013 | ||
| − | |v= | + | |v=0.50}} |
<tt>'''SymmetricInnerExtension'''</tt> is a [[List of functions|function]] that determines whether or not a given [[positive semidefinite]] operator is in the cone defined in reference <ref name="NOP09">M. Navascués, M. Owari, and M. B. Plenio. Complete Criterion for Separability Detection. <em>Physical Review Letters</em>, 103:160404, 2009. E-print: [http://arxiv.org/abs/0906.2735 arXiv:0906.2735] [quant-ph]</ref> that approximates the set of separable operators from the inside, based on operators with [[symmetric extension]]s. | <tt>'''SymmetricInnerExtension'''</tt> is a [[List of functions|function]] that determines whether or not a given [[positive semidefinite]] operator is in the cone defined in reference <ref name="NOP09">M. Navascués, M. Owari, and M. B. Plenio. Complete Criterion for Separability Detection. <em>Physical Review Letters</em>, 103:160404, 2009. E-print: [http://arxiv.org/abs/0906.2735 arXiv:0906.2735] [quant-ph]</ref> that approximates the set of separable operators from the inside, based on operators with [[symmetric extension]]s. | ||
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==Examples== | ==Examples== | ||
Please add some examples. | Please add some examples. | ||
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| + | {{SourceCode|name=SymmetricInnerExtension}} | ||
==References== | ==References== | ||
<references /> | <references /> | ||
Revision as of 15:29, 22 September 2014
| SymmetricInnerExtension | |
| Determines whether or not an operator has a symmetric inner extension | |
| Other toolboxes required | cvx |
|---|---|
| Related functions | IsPPT IsSeparable SymmetricExtension SymmetricProjection |
| Function category | Entanglement and separability |
SymmetricInnerExtension is a function that determines whether or not a given positive semidefinite operator is in the cone defined in reference [1] that approximates the set of separable operators from the inside, based on operators with symmetric extensions.
Syntax
- EX = SymmetricInnerExtension(X)
- EX = SymmetricInnerExtension(X,K)
- EX = SymmetricInnerExtension(X,K,DIM)
- EX = SymmetricInnerExtension(X,K,DIM,PPT)
- EX = SymmetricInnerExtension(X,K,DIM,PPT,TOL)
- [EX,WIT] = SymmetricInnerExtension(X,K,DIM,PPT,TOL)
Argument descriptions
Input arguments
- X: A positive semidefinite operator.
- K (optional, default 2): The number of copies of the second subsystem in the desired symmetric extension.
- DIM (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the two subsystems that X acts on.
- PPT (optional, default 1): A flag (either 1 or 0) that indicates whether or not the desired symmetric extension must have positive partial transpose.
- TOL (optional, default eps^(1/4)): The numerical tolerance used throughout this script. It is recommended that this is left at the default value unless numerical problems arise and the script has difficulty determining whether or not X has a symmetric inner extension.
Output arguments
- EX: A flag (either 1 or 0) indicating that X does or does not have a symmetric inner extension of the desired type. A value of 1 means that X is separable.
- WIT (optional): A witness that verifies that the answer provided by EX is correct. If EX = 1 (i.e., X is in the "inner" symmetric extension cone) then WIT is a symmetric extension of the operator \(\sigma_{AB}\) from [1], and thus acts as a witness that verifies that EX = 1 is correct. If X is not in this cone (i.e., EX = 0) then WIT is an operator with trace(WIT*X) = -1 but trace(WIT*Y) >= 0 for all operators in the described cone. Note that WIT may not be an entanglement witness!
Examples
Please add some examples.
Source code
Click here to view this function's source code on github.
References
- ↑ 1.0 1.1 M. Navascués, M. Owari, and M. B. Plenio. Complete Criterion for Separability Detection. Physical Review Letters, 103:160404, 2009. E-print: arXiv:0906.2735 [quant-ph]