ChessboardState - Revision history

Nathaniel at 18:34, 14 January 2015

2015-01-14T18:34:27Z

Nathaniel at 15:10, 29 September 2014

2014-09-29T15:10:58Z

Nathaniel: Created page with "{{Function |name=ChessboardState |desc=Produces a chessboard state |req=IsPPT
IsPSD
opt_args
PartialTranspose
PermuteSystems |upd=March..."

2013-06-24T20:10:57Z

Created page with "{{Function |name=ChessboardState |desc=Produces a chessboard state |req=IsPPT IsPSD opt_args PartialTranspose PermuteSystems |upd=March..."

New page

{{Function
|name=ChessboardState
|desc=Produces a chessboard state
|req=[[IsPPT]] [[IsPSD]] [[opt_args]] [[PartialTranspose]] [[PermuteSystems]]
|upd=March 13, 2013
|v=1.00}}
<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.

==Syntax==
* <tt>RHO = ChessboardState(A,B,C,D,M,N)</tt>
* <tt>RHO = ChessboardState(A,B,C,D,M,N,S,T)</tt>

==Argument descriptions==
* <tt>A,B,C,D,M,N</tt>: Six parameters that define chessboard states, as in <ref name="BP00"></ref>, with <tt>S = A*conj(C)/conj(N)</tt> and <tt>T = A*D/M</tt>. If <tt>C*M*conj(N)</tt> does not equal <tt>A*B*conj(C)</tt> then <tt>RHO</tt> is entangled. If each of <tt>A,B,C,D,M,N</tt> are real then <tt>RHO</tt> has positive partial transpose, and is hence bound entangled.
* <tt>S,T</tt>: Additional (optional) parameters of the chessboard states, also as in <ref name="BP00"></ref>. Note that, for certain choices of <tt>S</tt> and <tt>T</tt>, 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 state]]s. The following code generates a random chessboard state and verifies that it is entangled yet positive-partial-transpose (and hence bound entangled).
<pre<noinclude></noinclude>>
>> rho = ChessboardState(randn(1),randn(1),randn(1),randn(1),randn(1),randn(1));
>> [[IsSeparable|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|IsPPT(rho)]]

ans =

1
</pre<noinclude></noinclude>>

===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.
<pre>
>> rho = ChessboardState(1,2,3,4,5,6,7,8);
Warning: The specified chessboard state does not have positive partial transpose.
> In ChessboardState at 45
</pre>

==References==
<references />

@@ Line 2: / Line 2: @@
 |name=ChessboardState
 |desc=Produces a chessboard state
-|rel=[[IsPPT]]<br />[[PartialTranspose]]
+|rel=[[BreuerState]]<br />[[IsPPT]]<br />[[PartialTranspose]]
 |cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]]
 |upd=March 13, 2013

@@ Line 2: / Line 2: @@
 |name=ChessboardState
 |desc=Produces a chessboard state
-|req=[[IsPPT]]<br />[[IsPSD]]<br />[[opt_args]]<br />[[PartialTranspose]]<br />[[PermuteSystems]]
+|rel=[[IsPPT]]<br />[[PartialTranspose]]
 |upd=March 13, 2013
-|v=1.00}}
+|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.
@@ Line 18: / Line 19: @@
 ===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).
-<pre<noinclude></noinclude>>
+<syntaxhighlight>
 >> rho = ChessboardState(randn(1),randn(1),randn(1),randn(1),randn(1),randn(1));
->> [[IsSeparable|IsSeparable(rho)]]
+>> 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
@@ Line 29: / Line 30: @@
->> [[IsPPT|IsPPT(rho)]]
+>> IsPPT(rho)
 ans =
-</pre<noinclude></noinclude>>
+</syntaxhighlight>
 ===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 &ndash; a warning is produced in these cases.
-<pre>
+<syntaxhighlight>
 >> rho = ChessboardState(1,2,3,4,5,6,7,8);
 Warning: The specified chessboard state does not have positive partial transpose.
 > In ChessboardState at 45
-</pre>
+</syntaxhighlight>
 ==References==
 <references />

ChessboardState - Revision history

Nathaniel at 18:34, 14 January 2015

Nathaniel at 15:10, 29 September 2014

Nathaniel: Created page with "{{Function |name=ChessboardState |desc=Produces a chessboard state |req=IsPPTIsPSDopt_argsPartialTransposePermuteSystems |upd=March..."

Nathaniel: Created page with "{{Function |name=ChessboardState |desc=Produces a chessboard state |req=IsPPT
IsPSD
opt_args
PartialTranspose
PermuteSystems |upd=March..."