ChessboardState: Difference between revisions
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|name=ChessboardState | |name=ChessboardState | ||
|desc=Produces a chessboard state | |desc=Produces a chessboard state | ||
| | |rel=[[BreuerState]]<br />[[IsPPT]]<br />[[PartialTranspose]] | ||
|cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]] | |||
|upd=March 13, 2013 | |upd=March 13, 2013 | ||
|v= | |v=0.50}} | ||
<tt>'''ChessboardState'''</tt> is a [[List of functions|function]] that produces a two-qutrit "chessboard state", as defined in <ref name="BP00">D. Bruss and A. Peres. Construction of quantum states with bound entanglement. Phys. Rev. A, 61:30301(R), 2000. E-print: [http://arxiv.org/abs/quant-ph/9911056 arXiv:quant-ph/9911056]</ref>. These states are of interest because they are bound entangled. | <tt>'''ChessboardState'''</tt> is a [[List of functions|function]] that produces a two-qutrit "chessboard state", as defined in <ref name="BP00">D. Bruss and A. Peres. Construction of quantum states with bound entanglement. Phys. Rev. A, 61:30301(R), 2000. E-print: [http://arxiv.org/abs/quant-ph/9911056 arXiv:quant-ph/9911056]</ref>. These states are of interest because they are bound entangled. | ||
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===Generating bound entangled states=== | ===Generating bound entangled states=== | ||
Chessboard states are useful because they form a wide family of [[bound entangled state]]s. The following code generates a random chessboard state and verifies that it is entangled yet positive-partial-transpose (and hence bound entangled). | Chessboard states are useful because they form a wide family of [[bound entangled state]]s. The following code generates a random chessboard state and verifies that it is entangled yet positive-partial-transpose (and hence bound entangled). | ||
< | <syntaxhighlight> | ||
>> rho = ChessboardState(randn(1),randn(1),randn(1),randn(1),randn(1),randn(1)); | >> rho = ChessboardState(randn(1),randn(1),randn(1),randn(1),randn(1),randn(1)); | ||
>> | >> IsSeparable(rho) | ||
Determined to be entangled via the Filter Covariance Matrix Criterion. Reference: | Determined to be entangled via the Filter Covariance Matrix Criterion. Reference: | ||
O. Gittsovich, O. Gühne, P. Hyllus, and J. Eisert. Unifying several separability | O. Gittsovich, O. Gühne, P. Hyllus, and J. Eisert. Unifying several separability | ||
| Line 29: | Line 30: | ||
0 | 0 | ||
>> | >> IsPPT(rho) | ||
ans = | ans = | ||
1 | 1 | ||
</ | </syntaxhighlight> | ||
===When specifying <tt>S</tt> and <tt>T</tt>=== | ===When specifying <tt>S</tt> and <tt>T</tt>=== | ||
If you specify <tt>S</tt> and <tt>T</tt> manually, it is possible that the resulting state will not have positive partial transpose – a warning is produced in these cases. | If you specify <tt>S</tt> and <tt>T</tt> manually, it is possible that the resulting state will not have positive partial transpose – a warning is produced in these cases. | ||
< | <syntaxhighlight> | ||
>> rho = ChessboardState(1,2,3,4,5,6,7,8); | >> rho = ChessboardState(1,2,3,4,5,6,7,8); | ||
Warning: The specified chessboard state does not have positive partial transpose. | Warning: The specified chessboard state does not have positive partial transpose. | ||
> In ChessboardState at 45 | > In ChessboardState at 45 | ||
</ | </syntaxhighlight> | ||
{{SourceCode|name=ChessboardState}} | |||
==References== | ==References== | ||
<references /> | <references /> | ||
Latest revision as of 18:34, 14 January 2015
| ChessboardState | |
| Produces a chessboard state | |
| Other toolboxes required | none |
|---|---|
| Related functions | BreuerState IsPPT PartialTranspose |
| Function category | Special states, vectors, and operators |
ChessboardState is a function that produces a two-qutrit "chessboard state", as defined in [1]. These states are of interest because they are bound entangled.
Syntax
- RHO = ChessboardState(A,B,C,D,M,N)
- RHO = ChessboardState(A,B,C,D,M,N,S,T)
Argument descriptions
- A,B,C,D,M,N: Six parameters that define chessboard states, as in [1], with S = A*conj(C)/conj(N) and T = A*D/M. If C*M*conj(N) does not equal A*B*conj(C) then RHO is entangled. If each of A,B,C,D,M,N are real then RHO has positive partial transpose, and is hence bound entangled.
- S,T: Additional (optional) parameters of the chessboard states, also as in [1]. Note that, for certain choices of S and T, this state will not have positive partial transpose, and thus may not be bound entangled – a warning will be produced in these cases.
Examples
Generating bound entangled states
Chessboard states are useful because they form a wide family of bound entangled states. The following code generates a random chessboard state and verifies that it is entangled yet positive-partial-transpose (and hence bound entangled).
>> rho = ChessboardState(randn(1),randn(1),randn(1),randn(1),randn(1),randn(1));
>> IsSeparable(rho)
Determined to be entangled via the Filter Covariance Matrix Criterion. Reference:
O. Gittsovich, O. Gühne, P. Hyllus, and J. Eisert. Unifying several separability
conditions using the covariance matrix criterion. Phys. Rev. A, 78:052319, 2008.
ans =
0
>> IsPPT(rho)
ans =
1When specifying S and T
If you specify S and T manually, it is possible that the resulting state will not have positive partial transpose – a warning is produced in these cases.
>> rho = ChessboardState(1,2,3,4,5,6,7,8);
Warning: The specified chessboard state does not have positive partial transpose.
> In ChessboardState at 45Source code
Click here to view this function's source code on github.
References
- ↑ 1.0 1.1 1.2 D. Bruss and A. Peres. Construction of quantum states with bound entanglement. Phys. Rev. A, 61:30301(R), 2000. E-print: arXiv:quant-ph/9911056