SkVectorNorm - Revision history

Nathaniel: added CVX parameter

2014-12-24T16:49:09Z

added CVX parameter

← Older revision		Revision as of 16:49, 24 December 2014
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	{{Function		{{Function
	\|name=SkVectorNorm		\|name=SkVectorNorm
	\|desc=Computes the ~~[[s(k)-vector norm\|~~s(k)-norm of a vector]]		\|desc=Computes the s(k)-norm of a vector
	\|rel=[[KyFanNorm]]<br />[[SchmidtDecomposition]]<br />[[SkOperatorNorm]]		\|rel=[[KyFanNorm]]<br />[[SchmidtDecomposition]]<br />[[SkOperatorNorm]]
	\|cat=[[List of functions#Norms\|Norms]]		\|cat=[[List of functions#Norms\|Norms]]
	\|upd=December 2, 2012		\|upd=December 2, 2012
	\|v=~~0.50~~}}		\|cvx=no}}
	<tt>'''SkVectorNorm'''</tt> is a [[List of functions\|function]] that computes the ~~[[s(k)-vector norm\|~~s(k)-norm of a vector]] (i.e., the Euclidean norm of the vector of its k largest [[Schmidt coefficients]]<ref>N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. ''J. Math. Phys.'', 51:082202, 2010. E-print: [http://arxiv.org/abs/0909.3907 arXiv:0909.3907] [quant-ph]</ref>).		<tt>'''SkVectorNorm'''</tt> is a [[List of functions\|function]] that computes the s(k)-norm of a vector (i.e., the Euclidean norm of the vector of its k largest Schmidt coefficients<ref>N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. ''J. Math. Phys.'', 51:082202, 2010. E-print: [http://arxiv.org/abs/0909.3907 arXiv:0909.3907] [quant-ph]</ref>).

	==Syntax==		==Syntax==
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	==Argument descriptions==		==Argument descriptions==
	* <tt>VEC</tt>: A vector living in [[bipartite]] space.		* <tt>VEC</tt>: A vector living in bipartite space.
	* <tt>K</tt> (optional, default 1): A positive integer.		* <tt>K</tt> (optional, default 1): A positive integer.
	* <tt>DIM</tt> (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the subsystems that <tt>VEC</tt> lives on.		* <tt>DIM</tt> (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the subsystems that <tt>VEC</tt> lives on.
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	==Examples==		==Examples==
	===Sum of squares of eigenvalues of reduced density matrix===		===Sum of squares of eigenvalues of reduced density matrix===
	The square of the s(k)-vector norm is equal to the ~~[[Ky Fan norm\|~~Ky Fan k-norm]] of the vector's reduced density matrix:		The square of the s(k)-vector norm is equal to the Ky Fan k-norm of the vector's reduced density matrix:
	<syntaxhighlight>		<syntaxhighlight>
	>> v = RandomStateVector(9);		>> v = RandomStateVector(9);

Nathaniel at 17:16, 22 September 2014

2014-09-22T17:16:09Z

← Older revision		Revision as of 17:16, 22 September 2014
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	\|name=SkVectorNorm		\|name=SkVectorNorm
	\|desc=Computes the [[s(k)-vector norm\|s(k)-norm of a vector]]		\|desc=Computes the [[s(k)-vector norm\|s(k)-norm of a vector]]
	\|~~req~~=[[~~opt_args~~]]<br />[[SchmidtDecomposition]]		\|rel=[[KyFanNorm]]<br />[[SchmidtDecomposition]]<br />[[SkOperatorNorm]]
	~~\|rel=[[KyFanNorm~~]]<br />[[SkOperatorNorm]]		\|cat=[[List of functions#Norms\|Norms]]
	\|upd=December 2, 2012		\|upd=December 2, 2012
	\|v=1.01}}		\|v=0.50}}
	<tt>'''SkVectorNorm'''</tt> is a [[List of functions\|function]] that computes the [[s(k)-vector norm\|s(k)-norm of a vector]] (i.e., the Euclidean norm of the vector of its k largest [[Schmidt coefficients]]<ref>N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. ''J. Math. Phys.'', 51:082202, 2010. E-print: [http://arxiv.org/abs/0909.3907 arXiv:0909.3907] [quant-ph]</ref>).		<tt>'''SkVectorNorm'''</tt> is a [[List of functions\|function]] that computes the [[s(k)-vector norm\|s(k)-norm of a vector]] (i.e., the Euclidean norm of the vector of its k largest [[Schmidt coefficients]]<ref>N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. ''J. Math. Phys.'', 51:082202, 2010. E-print: [http://arxiv.org/abs/0909.3907 arXiv:0909.3907] [quant-ph]</ref>).

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	===Sum of squares of eigenvalues of reduced density matrix===		===Sum of squares of eigenvalues of reduced density matrix===
	The square of the s(k)-vector norm is equal to the [[Ky Fan norm\|Ky Fan k-norm]] of the vector's reduced density matrix:		The square of the s(k)-vector norm is equal to the [[Ky Fan norm\|Ky Fan k-norm]] of the vector's reduced density matrix:
	<~~pre<noinclude></noinclude>~~>		<syntaxhighlight>
	>> v = ~~[[RandomStateVector\|~~RandomStateVector(9)]];		>> v = RandomStateVector(9);
	>> [SkVectorNorm(v,1)^2, [[KyFanNorm]]([[PartialTrace]](v*v'),1)]		>> [SkVectorNorm(v,1)^2, KyFanNorm(PartialTrace(v*v'),1)]

	ans =		ans =
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	1.0000 1.0000		1.0000 1.0000
	</~~pre<noinclude></noinclude>~~>		</syntaxhighlight>

			{{SourceCode\|name=SkVectorNorm}}

	==References==		==References==
	<references />		<references />

Nathaniel: Uploaded v1.01

2012-12-02T15:34:05Z

Uploaded v1.01

← Older revision		Revision as of 15:34, 2 December 2012
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	\|req=[[opt_args]]<br />[[SchmidtDecomposition]]		\|req=[[opt_args]]<br />[[SchmidtDecomposition]]
	\|rel=[[KyFanNorm]]<br />[[SkOperatorNorm]]		\|rel=[[KyFanNorm]]<br />[[SkOperatorNorm]]
	\|upd=~~November 18~~, 2012		\|upd=December 2, 2012
	\|v=1.00}}		\|v=1.01}}
	<tt>'''SkVectorNorm'''</tt> is a [[List of functions\|function]] that computes the [[s(k)-vector norm\|s(k)-norm of a vector]] (i.e., the Euclidean norm of the vector of its k largest [[Schmidt coefficients]]<ref>N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. ''J. Math. Phys.'', 51:082202, 2010.</ref>).		<tt>'''SkVectorNorm'''</tt> is a [[List of functions\|function]] that computes the [[s(k)-vector norm\|s(k)-norm of a vector]] (i.e., the Euclidean norm of the vector of its k largest [[Schmidt coefficients]]<ref>N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. ''J. Math. Phys.'', 51:082202, 2010. E-print: [http://arxiv.org/abs/0909.3907 arXiv:0909.3907] [quant-ph]</ref>).

	==Syntax==		==Syntax==

Nathaniel: Created page with "{{Function |name=SkVectorNorm |desc=Computes the s(k)-norm of a vector |req=opt_args
SchmidtDecomposition |rel=KyFanNorm
[[SkOperato..."

2012-12-02T15:32:41Z

Created page with "{{Function |name=SkVectorNorm |desc=Computes the s(k)-norm of a vector |req=opt_args<br />SchmidtDecomposition |rel=KyFanNorm<br />[[SkOperato..."

New page

{{Function
|name=SkVectorNorm
|desc=Computes the [[s(k)-vector norm|s(k)-norm of a vector]]
|req=[[opt_args]]<br />[[SchmidtDecomposition]]
|rel=[[KyFanNorm]]<br />[[SkOperatorNorm]]
|upd=November 18, 2012
|v=1.00}}
<tt>'''SkVectorNorm'''</tt> is a [[List of functions|function]] that computes the [[s(k)-vector norm|s(k)-norm of a vector]] (i.e., the Euclidean norm of the vector of its k largest [[Schmidt coefficients]]<ref>N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. ''J. Math. Phys.'', 51:082202, 2010.</ref>).

==Syntax==
* <tt>SkVectorNorm(VEC)</tt>
* <tt>SkVectorNorm(VEC,K)</tt>
* <tt>SkVectorNorm(VEC,K,DIM)</tt>

==Argument descriptions==
* <tt>VEC</tt>: A vector living in [[bipartite]] space.
* <tt>K</tt> (optional, default 1): A positive integer.
* <tt>DIM</tt> (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the subsystems that <tt>VEC</tt> lives on.

==Examples==
===Sum of squares of eigenvalues of reduced density matrix===
The square of the s(k)-vector norm is equal to the [[Ky Fan norm|Ky Fan k-norm]] of the vector's reduced density matrix:
<pre<noinclude></noinclude>>
>> v = [[RandomStateVector|RandomStateVector(9)]];
>> [SkVectorNorm(v,1)^2, [[KyFanNorm]]([[PartialTrace]](v*v'),1)]

ans =

0.7754 0.7754

>> [SkVectorNorm(v,2)^2, KyFanNorm(PartialTrace(v*v'),2)]

ans =

0.9333 0.9333

>> [SkVectorNorm(v,3)^2, KyFanNorm(PartialTrace(v*v'),3)]

ans =

1.0000 1.0000
</pre<noinclude></noinclude>>

==References==
<references />

SkVectorNorm - Revision history

Nathaniel: added CVX parameter

Nathaniel at 17:16, 22 September 2014

Nathaniel: Uploaded v1.01

Nathaniel: Created page with "{{Function |name=SkVectorNorm |desc=Computes the s(k)-norm of a vector |req=opt_argsSchmidtDecomposition |rel=KyFanNorm[[SkOperato..."

Nathaniel: Created page with "{{Function |name=SkVectorNorm |desc=Computes the s(k)-norm of a vector |req=opt_args
SchmidtDecomposition |rel=KyFanNorm
[[SkOperato..."