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Nathaniel: LaTeX fix

2023-08-01T01:54:15Z

LaTeX fix

Nathaniel: Changing syntax highlighting

2022-05-26T14:13:40Z

Changing syntax highlighting

Nathaniel: Update syntaxhighlight tag

2022-05-26T12:25:52Z

Update syntaxhighlight tag

Nathaniel: typo

2016-04-04T15:00:34Z

typo

Nathaniel: Moved download box to template

2015-01-14T17:30:04Z

Moved download box to template

Nathaniel: Fixed download link when clicking on image

2014-12-15T19:18:17Z

Fixed download link when clicking on image

Nathaniel: Updated to v0.6

2014-11-28T02:17:58Z

Updated to v0.6

Nathaniel: Updated download link to latest stable release

2014-11-12T17:15:54Z

Updated download link to latest stable release

Nathaniel: Added pure state examples

2014-11-12T16:44:26Z

Added pure state examples

Nathaniel at 21:16, 7 November 2014

2014-11-07T21:16:58Z

@@ Line 55: / Line 55: @@
 QETLAB can also handle mixed state entanglement without trouble. To demonstrate these features, let's start by creating a bound entangled state and then detecting its entanglement.
-One well-known way to create bound entangled states is via unextendible product bases (UPBs)<ref name="BDM99">C.H. Bennett, D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases and bound entanglement. ''Phys. Rev. Lett.'' 82, 5385&ndash;5388, 1999. E-print: [http://arxiv.org/abs/quant-ph/9808030 arXiv:quant-ph/9808030]</ref><ref name="DMS03">D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases, uncompletable product bases and bound entanglement. ''Commun. Math. Phys.'' 238, 379&ndash;410, 2003. E-print: [http://arxiv.org/abs/quant-ph/9908070 arXiv:quant-ph/9908070]</ref>. Let's first generate the "Tiles" UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ and construct a bound entangled state from it:
+One well-known way to create bound entangled states is via unextendible product bases (UPBs)<ref name="BDM99">C.H. Bennett, D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases and bound entanglement. ''Phys. Rev. Lett.'' 82, 5385&ndash;5388, 1999. E-print: [http://arxiv.org/abs/quant-ph/9808030 arXiv:quant-ph/9808030]</ref><ref name="DMS03">D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases, uncompletable product bases and bound entanglement. ''Commun. Math. Phys.'' 238, 379&ndash;410, 2003. E-print: [http://arxiv.org/abs/quant-ph/9908070 arXiv:quant-ph/9908070]</ref>. Let's first generate the "Tiles" UPB in <math>\mathbb{C}^3 \otimes \mathbb{C}^3</math> and construct a bound entangled state from it:
 <code><nowiki>>> u = </nowiki>[[UPB]]<nowiki>('Tiles') % generate the "Tiles" unextendible product basis

@@ Line 8: / Line 8: @@
 ===Pure state entanglement and the Schmidt decomposition===
 The heart of QETLAB is a suite of functions that make working with quantum entanglement quick and easy. Working with pure state entanglement is a breeze, as demonstrated by the following code snippet, which generates a random pure state (according to uniform spherical measure/Haar measure) and computes its Schmidt decomposition:
-<syntaxhighlight lang="matlab">
+<code><nowiki>>> d = 3; % this example will be in 3 \otimes 3 dimensions
->> d = 3; % this example will be in 3 \otimes 3 dimensions
+>> phi = </nowiki>[[RandomStateVector]]<nowiki>(d^2);
->> phi = RandomStateVector(d^2);
+>> [s,a,b] = </nowiki>[[SchmidtDecomposition]]<nowiki>(phi)
 s =
@@ Line 32: / Line 31: @@
    -0.2513 + 0.1492i  -0.3837 + 0.3479i   0.0874 - 0.7992i
 .5520 - 0.6828i  -0.3670 + 0.2737i  -0.1378 - 0.0208i
-</syntaxhighlight>
+</nowiki></code>
 We could verify that this Schmidt decomposition is correct as follows:
-<syntaxhighlight lang="matlab">
+<code><nowiki>>> phi2 = s(1)*kron(a(:,1),b(:,1)) + s(2)*kron(a(:,2),b(:,2)) + s(3)*kron(a(:,3),b(:,3));
 >> norm(phi - phi2)
@@ Line 43: / Line 41: @@
 .8378e-016
-</syntaxhighlight>
+</nowiki></code>
 However, QETLAB has a [[TensorSum|built-in function]] that acts as the inverse of the Schmidt decomposition, to make this process easier:
-<syntaxhighlight lang="matlab">
+<code><nowiki>>> phi3 = </nowiki>[[TensorSum]]<nowiki>(s,a,b);
 >> norm(phi - phi3)
@@ Line 53: / Line 50: @@
 .8378e-016
-</syntaxhighlight>
+</nowiki></code>
 ===Mixed state entanglement and detecting bound entanglement===
@@ Line 59: / Line 56: @@
 One well-known way to create bound entangled states is via unextendible product bases (UPBs)<ref name="BDM99">C.H. Bennett, D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases and bound entanglement. ''Phys. Rev. Lett.'' 82, 5385&ndash;5388, 1999. E-print: [http://arxiv.org/abs/quant-ph/9808030 arXiv:quant-ph/9808030]</ref><ref name="DMS03">D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases, uncompletable product bases and bound entanglement. ''Commun. Math. Phys.'' 238, 379&ndash;410, 2003. E-print: [http://arxiv.org/abs/quant-ph/9908070 arXiv:quant-ph/9908070]</ref>. Let's first generate the "Tiles" UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ and construct a bound entangled state from it:
-<syntaxhighlight lang="matlab">
+<code><nowiki>>> u = </nowiki>[[UPB]]<nowiki>('Tiles') % generate the "Tiles" unextendible product basis
 u =
@@ Line 76: / Line 72: @@
 >> rho = eye(9) - u*u'; % rho is the projection onto the orthogonal complement of the UPB vectors
 >> rho = rho/trace(rho); % scale rho to have trace 1
-</syntaxhighlight>
+</nowiki></code>
 Now <tt>rho</tt> is a bound entangled state. We can verify this in QETLAB as follows:
-<syntaxhighlight lang="matlab">
+<code><nowiki>>> </nowiki>[[IsPPT]]<nowiki>(rho) % this will show that rho has positive partial transpose
 ans =
@@ Line 86: / Line 81: @@
->> IsSeparable(rho) % this will show that rho is entangled
+>> </nowiki>[[IsSeparable]]<nowiki>(rho) % this will show that rho is entangled
 Determined to be entangled via the realignment criterion. Reference:
@@ Line 94: / Line 89: @@
-</syntaxhighlight>
+</nowiki></code>
 QETLAB can also carry out many related functions, such as [[SymmetricExtension|finding entanglement witnesses that detect entanglement in a given state]], [[IsBlockPositive|determining whether or not a given operator is an entanglement witness]], and [[IsUPB|deciding whether or not a given set of vectors form an unextendible product basis]]. Furthermore, there are numerous examples scattered throughout the documentation that make learning how to carry out these operations a breeze.

@@ Line 8: / Line 8: @@
 ===Pure state entanglement and the Schmidt decomposition===
 The heart of QETLAB is a suite of functions that make working with quantum entanglement quick and easy. Working with pure state entanglement is a breeze, as demonstrated by the following code snippet, which generates a random pure state (according to uniform spherical measure/Haar measure) and computes its Schmidt decomposition:
-<syntaxhighlight>
+<syntaxhighlight lang="matlab">
 >> d = 3; % this example will be in 3 \otimes 3 dimensions
 >> phi = RandomStateVector(d^2);
@@ Line 36: / Line 36: @@
 We could verify that this Schmidt decomposition is correct as follows:
-<syntaxhighlight>
+<syntaxhighlight lang="matlab">
 >> phi2 = s(1)*kron(a(:,1),b(:,1)) + s(2)*kron(a(:,2),b(:,2)) + s(3)*kron(a(:,3),b(:,3));
 >> norm(phi - phi2)
@@ Line 46: / Line 46: @@
 However, QETLAB has a [[TensorSum|built-in function]] that acts as the inverse of the Schmidt decomposition, to make this process easier:
-<syntaxhighlight>
+<syntaxhighlight lang="matlab">
 >> phi3 = TensorSum(s,a,b);
 >> norm(phi - phi3)
@@ Line 59: / Line 59: @@
 One well-known way to create bound entangled states is via unextendible product bases (UPBs)<ref name="BDM99">C.H. Bennett, D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases and bound entanglement. ''Phys. Rev. Lett.'' 82, 5385&ndash;5388, 1999. E-print: [http://arxiv.org/abs/quant-ph/9808030 arXiv:quant-ph/9808030]</ref><ref name="DMS03">D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases, uncompletable product bases and bound entanglement. ''Commun. Math. Phys.'' 238, 379&ndash;410, 2003. E-print: [http://arxiv.org/abs/quant-ph/9908070 arXiv:quant-ph/9908070]</ref>. Let's first generate the "Tiles" UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ and construct a bound entangled state from it:
-<syntaxhighlight>
+<syntaxhighlight lang="matlab">
 >> u = UPB('Tiles') % generate the "Tiles" unextendible product basis
@@ Line 79: / Line 79: @@
 Now <tt>rho</tt> is a bound entangled state. We can verify this in QETLAB as follows:
-<syntaxhighlight>
+<syntaxhighlight lang="matlab">
 >> IsPPT(rho) % this will show that rho has positive partial transpose

@@ Line 56: / Line 56: @@
 ===Mixed state entanglement and detecting bound entanglement===
-QETLAB can also hand mixed state entanglement without trouble. To demonstrate these features, let's start by creating a bound entangled state and then detecting its entanglement.
+QETLAB can also handle mixed state entanglement without trouble. To demonstrate these features, let's start by creating a bound entangled state and then detecting its entanglement.
 One well-known way to create bound entangled states is via unextendible product bases (UPBs)<ref name="BDM99">C.H. Bennett, D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases and bound entanglement. ''Phys. Rev. Lett.'' 82, 5385&ndash;5388, 1999. E-print: [http://arxiv.org/abs/quant-ph/9808030 arXiv:quant-ph/9808030]</ref><ref name="DMS03">D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases, uncompletable product bases and bound entanglement. ''Commun. Math. Phys.'' 238, 379&ndash;410, 2003. E-print: [http://arxiv.org/abs/quant-ph/9908070 arXiv:quant-ph/9908070]</ref>. Let's first generate the "Tiles" UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ and construct a bound entangled state from it:

← Older revision		Revision as of 17:30, 14 January 2015
Line 2:		Line 2:
	'''QETLAB''' ('''Q'''uantum '''E'''ntanglement '''T'''heory '''LAB'''oratory) is a MATLAB toolbox for exploring quantum entanglement theory. While there are many quantum information theory toolboxes that allow the user to perform basic operations such as the [[PartialTranspose\|partial transposition]], new tests are constantly discovered. The goal of QETLAB is to remain up-to-date and contain an ever-growing catalogue of separability criteria, positive maps, and related functions of interest. Furthermore, QETLAB is designed to work well both with full matrices and with large sparse matrices, and makes use of many advanced techniques based on semidefinite programming.		'''QETLAB''' ('''Q'''uantum '''E'''ntanglement '''T'''heory '''LAB'''oratory) is a MATLAB toolbox for exploring quantum entanglement theory. While there are many quantum information theory toolboxes that allow the user to perform basic operations such as the [[PartialTranspose\|partial transposition]], new tests are constantly discovered. The goal of QETLAB is to remain up-to-date and contain an ever-growing catalogue of separability criteria, positive maps, and related functions of interest. Furthermore, QETLAB is designed to work well both with full matrices and with large sparse matrices, and makes use of many advanced techniques based on semidefinite programming.

−	~~<div style="border:2px outset #dddddd;background:#eeeeee;margin:12px auto 5px auto;padding:5px;white-space:nowrap;width:75%;min-width:620px;">~~	+	{{DownloadBox}}
−	{~~\| style="background:#eeeeee;" \|~~
−	\|-
−	~~\| valign="top" \| [[File:download.gif\|link=https://github.com/nathanieljohnston/QETLAB/archive/v0.6.zip]]~~
−	\|<span style="padding-left:10px;font-size:130%;font-weight:bold;">Download and Install QETLAB</span><br /><div style="padding:4px 0 0 12px;">'''Step 1:''' Download [https://github.com/nathanieljohnston/QETLAB/archive/v0.6.zip QETLAB] (current version: 0.60, last updated: November 27, 2014)</div><div style="padding:4px 0 0 12px;">'''Step 2:''' Unzip the file in your MATLAB scripts directory</div><div style="padding:4px 0 0 12px;">'''Step 3:''' Download and install [http://cvxr.com/cvx/ CVX]</div><div style="font-size:90%; padding:8px 0 0 12px;">If you need more detailed installation instructions, [[Installation\|click here]].</div>
−	\|}~~</div>~~

@@ Line 5: / Line 5: @@
 {| style="background:#eeeeee;" |
 |-
-| valign="top" | [[File:download.gif|link=https://github.com/nathanieljohnston/qetlab/zipball/master]]
+| valign="top" | [[File:download.gif|link=https://github.com/nathanieljohnston/QETLAB/archive/v0.6.zip]]
 |<span style="padding-left:10px;font-size:130%;font-weight:bold;">Download and Install QETLAB</span><br /><div style="padding:4px 0 0 12px;">'''Step 1:''' Download [https://github.com/nathanieljohnston/QETLAB/archive/v0.6.zip QETLAB] (current version: 0.60, last updated: November 27, 2014)</div><div style="padding:4px 0 0 12px;">'''Step 2:''' Unzip the file in your MATLAB scripts directory</div><div style="padding:4px 0 0 12px;">'''Step 3:''' Download and install [http://cvxr.com/cvx/ CVX]</div><div style="font-size:90%; padding:8px 0 0 12px;">If you need more detailed installation instructions, [[Installation|click here]].</div>
 |}</div>

@@ Line 6: / Line 6: @@
 |-
 | valign="top" | [[File:download.gif|link=https://github.com/nathanieljohnston/qetlab/zipball/master]]
-|<span style="padding-left:10px;font-size:130%;font-weight:bold;">Download and Install QETLAB</span><br /><div style="padding:4px 0 0 12px;">'''Step 1:''' Download [https://github.com/nathanieljohnston/qetlab/zipball/master QETLAB] (current version: 0.50, last updated: November 6, 2014)</div><div style="padding:4px 0 0 12px;">'''Step 2:''' Unzip the file in your MATLAB scripts directory</div><div style="padding:4px 0 0 12px;">'''Step 3:''' Download and install [http://cvxr.com/cvx/ CVX]</div><div style="font-size:90%; padding:8px 0 0 12px;">If you need more detailed installation instructions, [[Installation|click here]].</div>
+|<span style="padding-left:10px;font-size:130%;font-weight:bold;">Download and Install QETLAB</span><br /><div style="padding:4px 0 0 12px;">'''Step 1:''' Download [https://github.com/nathanieljohnston/QETLAB/archive/v0.5.zip QETLAB] (current version: 0.50, last updated: November 6, 2014)</div><div style="padding:4px 0 0 12px;">'''Step 2:''' Unzip the file in your MATLAB scripts directory</div><div style="padding:4px 0 0 12px;">'''Step 3:''' Download and install [http://cvxr.com/cvx/ CVX]</div><div style="font-size:90%; padding:8px 0 0 12px;">If you need more detailed installation instructions, [[Installation|click here]].</div>
 |}</div>

@@ Line 1: / Line 1: @@
 __NOTOC____NOEDITSECTION__== QETLAB: A MATLAB Toolbox for Quantum Entanglement ==
-<div style="float:right;border:1px outset #dddddd;background:#eeeeee;margin:12px 20px 5px 20px;padding:5px;white-space:nowrap;">
+<div style="border:2px outset #dddddd;background:#eeeeee;margin:12px auto 5px auto;padding:5px;white-space:nowrap;width:75%;min-width:620px;">
 {| style="background:#eeeeee;" |
 |-
@@ Line 8: / Line 9: @@
 |}</div>
-'''QETLAB''' ('''Q'''uantum '''E'''ntanglement '''T'''heory '''LAB'''oratory) is a MATLAB toolbox for exploring quantum entanglement theory. While there are many quantum information theory toolboxes that allow the user to perform basic operations such as the [[PartialTranspose|partial transposition]], new tests are constantly discovered. The goal of QETLAB is to remain up-to-date and contain an ever-growing catalogue of separability criteria, positive maps, and related functions of interest. Furthermore, QETLAB is designed to work well both with full matrices and with large sparse matrices, and makes use of many advanced techniques based on semidefinite programming.
+==Getting started: some introductory examples==
 ===Pure state entanglement and the Schmidt decomposition===
 I will fill this in shortly.
-===Mixed state entanglement: detecting bound entanglement===
+===Mixed state entanglement and detecting bound entanglement===
 The heart of QETLAB is a suite of functions that make working with quantum entanglement quick and easy. To get a feel for what types of functions QETLAB provides, let's start by creating a bound entangled state and then detecting its entanglement.