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Nathaniel: LaTeX fix

2023-08-01T01:54:15Z

LaTeX fix

← Older revision		Revision as of 01:54, 1 August 2023
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	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.		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, 5385–5388, 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, 379–410, 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, 5385–5388, 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, 379–410, 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		<code><nowiki>>> u = </nowiki>[[UPB]]<nowiki>('Tiles') % generate the "Tiles" unextendible product basis

Nathaniel: Changing syntax highlighting

2022-05-26T14:13:40Z

Changing syntax highlighting

← Older revision		Revision as of 14:13, 26 May 2022
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	===Pure state entanglement and the Schmidt decomposition===		===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:		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,a,b] = SchmidtDecomposition(phi)

	s =		s =
Line 32:		Line 31:
	-0.2513 + 0.1492i -0.3837 + 0.3479i 0.0874 - 0.7992i		-0.2513 + 0.1492i -0.3837 + 0.3479i 0.0874 - 0.7992i
	0.5520 - 0.6828i -0.3670 + 0.2737i -0.1378 - 0.0208i		0.5520 - 0.6828i -0.3670 + 0.2737i -0.1378 - 0.0208i
	</~~syntaxhighlight~~>		</nowiki></code>

	We could verify that this Schmidt decomposition is correct as follows:		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));
	>> 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)		>> norm(phi - phi2)

Line 43:		Line 41:

	5.8378e-016		5.8378e-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:		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);
	>> phi3 = TensorSum(s,a,b);
	>> norm(phi - phi3)		>> norm(phi - phi3)

Line 53:		Line 50:

	5.8378e-016		5.8378e-016
	</~~syntaxhighlight~~>		</nowiki></code>

	===Mixed state entanglement and detecting bound entanglement===		===Mixed state entanglement and detecting bound entanglement===
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	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, 5385–5388, 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, 379–410, 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, 5385–5388, 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, 379–410, 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 = UPB('Tiles') % generate the "Tiles" unextendible product basis

	u =		u =
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	>> rho = eye(9) - u*u'; % rho is the projection onto the orthogonal complement of the UPB vectors		>> 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		>> 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:		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
	>> IsPPT(rho) % this will show that rho has positive partial transpose

	ans =		ans =
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	1		1

	>> 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:		Determined to be entangled via the realignment criterion. Reference:
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	0		0
	</~~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.		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.

Nathaniel: Update syntaxhighlight tag

2022-05-26T12:25:52Z

Update syntaxhighlight tag

← Older revision		Revision as of 12:25, 26 May 2022
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	===Pure state entanglement and the Schmidt decomposition===		===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:		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		>> d = 3; % this example will be in 3 \otimes 3 dimensions
	>> phi = RandomStateVector(d^2);		>> phi = RandomStateVector(d^2);
Line 36:		Line 36:
	We could verify that this Schmidt decomposition is correct as follows:		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));		>> 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)		>> 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:		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);		>> phi3 = TensorSum(s,a,b);
	>> norm(phi - phi3)		>> 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, 5385–5388, 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, 379–410, 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, 5385–5388, 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, 379–410, 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		>> u = UPB('Tiles') % generate the "Tiles" unextendible product basis

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	Now <tt>rho</tt> is a bound entangled state. We can verify this in QETLAB as follows:		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		>> IsPPT(rho) % this will show that rho has positive partial transpose

Nathaniel: typo

2016-04-04T15:00:34Z

typo

← Older revision		Revision as of 15:00, 4 April 2016
Line 56:		Line 56:

	===Mixed state entanglement and detecting bound entanglement===		===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, 5385–5388, 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, 379–410, 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, 5385–5388, 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, 379–410, 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:

Nathaniel: Moved download box to template

2015-01-14T17:30:04Z

Moved download box to template

← Older revision		Revision as of 17:30, 14 January 2015
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	'''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>~~

Nathaniel: Fixed download link when clicking on image

2014-12-15T19:18:17Z

Fixed download link when clicking on image

← Older revision		Revision as of 19:18, 15 December 2014
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	{\| style="background:#eeeeee;" \|		{\| 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>		\|<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>		\|}</div>

Nathaniel: Updated to v0.6

2014-11-28T02:17:58Z

Updated to v0.6

← Older revision		Revision as of 02:17, 28 November 2014
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	\|-		\|-
	\| valign="top" \| [[File:download.gif\|link=https://github.com/nathanieljohnston/qetlab/zipball/master]]		\| 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/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>		\|<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>		\|}</div>

Nathaniel: Updated download link to latest stable release

2014-11-12T17:15:54Z

Updated download link to latest stable release

← Older revision		Revision as of 17:15, 12 November 2014
Line 6:		Line 6:
	\|-		\|-
	\| valign="top" \| [[File:download.gif\|link=https://github.com/nathanieljohnston/qetlab/zipball/master]]		\| 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>		\|}</div>

Nathaniel: Added pure state examples

2014-11-12T16:44:26Z

Added pure state examples

@@ Line 8: / Line 8: @@
 |<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>
 |}</div>
 ==Getting started: some introductory examples==
 ===Pure state entanglement and the Schmidt decomposition===
-I will fill this in shortly.
+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:
 ===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.
+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.
 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:

Nathaniel at 21:16, 7 November 2014

2014-11-07T21:16:58Z

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	__NOTOC____NOEDITSECTION__== QETLAB: A MATLAB Toolbox for Quantum Entanglement ==		__NOTOC____NOEDITSECTION__== QETLAB: A MATLAB Toolbox for Quantum Entanglement ==
			'''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.

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	'''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==

	==~~Some~~ introductory examples==
	===Pure state entanglement and the Schmidt decomposition===		===Pure state entanglement and the Schmidt decomposition===
	I will fill this in shortly.		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.		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.