CBNorm - Revision history

Rmmateri at 16:39, 13 June 2018

2018-06-13T16:39:54Z

← Older revision		Revision as of 16:39, 13 June 2018
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	\|name=CBNorm		\|name=CBNorm
	\|desc=Computes the completely bounded norm of a superoperator		\|desc=Computes the completely bounded norm of a superoperator
	\|req=[http://cvxr.com/cvx/ ~~cvx~~]		\|req=[http://cvxr.com/cvx/ CVX]
	\|rel=[[DiamondNorm]]<br />[[InducedSchattenNorm]]		\|rel=[[DiamondNorm]]<br />[[InducedSchattenNorm]]
	\|cat=[[List of functions#Norms\|Norms]]		\|cat=[[List of functions#Norms\|Norms]]

Nathaniel at 00:22, 12 January 2016

2016-01-12T00:22:48Z

← Older revision		Revision as of 00:22, 12 January 2016
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	\|desc=Computes the completely bounded norm of a superoperator		\|desc=Computes the completely bounded norm of a superoperator
	\|req=[http://cvxr.com/cvx/ cvx]		\|req=[http://cvxr.com/cvx/ cvx]
	\|rel=[[DiamondNorm]]		\|rel=[[DiamondNorm]]<br />[[InducedSchattenNorm]]
	\|cat=[[List of functions#Norms\|Norms]]		\|cat=[[List of functions#Norms\|Norms]]
	\|upd=November 21, 2014		\|upd=November 21, 2014

Nathaniel: added CVX parameter

2014-12-24T16:35:56Z

added CVX parameter

← Older revision		Revision as of 16:35, 24 December 2014
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	\|rel=[[DiamondNorm]]		\|rel=[[DiamondNorm]]
	\|cat=[[List of functions#Norms\|Norms]]		\|cat=[[List of functions#Norms\|Norms]]
	\|upd=November 21, 2014}}		\|upd=November 21, 2014
			\|cvx=yes (convex)}}
	<tt>'''CBNorm'''</tt> is a [[List of functions\|function]] that computes the completely bounded (CB) norm $\\|\Phi\\|_{cb}$ of a superoperator $\Phi$.		<tt>'''CBNorm'''</tt> is a [[List of functions\|function]] that computes the completely bounded (CB) norm $\\|\Phi\\|_{cb}$ of a superoperator $\Phi$.

Nathaniel: Updated for CVX functionality

2014-11-27T21:35:04Z

Updated for CVX functionality

← Older revision		Revision as of 21:35, 27 November 2014
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	{{Function		{{Function
	\|name=CBNorm		\|name=CBNorm
	\|desc=Computes the [[completely bounded norm]] of a superoperator		\|desc=Computes the completely bounded norm of a superoperator
	\|req=[http://cvxr.com/cvx/ cvx]		\|req=[http://cvxr.com/cvx/ cvx]
	\|rel=[[DiamondNorm]]		\|rel=[[DiamondNorm]]
	\|cat=[[List of functions#Norms\|Norms]]		\|cat=[[List of functions#Norms\|Norms]]
	\|upd=~~January 22~~, ~~2013~~		\|upd=November 21, 2014}}
	~~\|v=0.50~~}}		<tt>'''CBNorm'''</tt> is a [[List of functions\|function]] that computes the completely bounded (CB) norm $\\|\Phi\\|_{cb}$ of a superoperator $\Phi$.
	<tt>'''CBNorm'''</tt> is a [[List of functions\|function]] that computes the ~~[[completely bounded norm\|~~completely bounded (CB) norm]] $\\|\Phi\\|_{cb}$ of a superoperator $\Phi$.

	==Syntax==		==Syntax==
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	==Argument descriptions==		==Argument descriptions==
	* <tt>PHI</tt>: A superoperator. Should be provided as either a [[Choi matrix]], or as a cell with either 1 or 2 columns (see the [[tutorial]] page for more details about specifying superoperators within QETLAB).		* <tt>PHI</tt>: A superoperator. Should be provided as either a Choi matrix, or as a cell with either 1 or 2 columns (see the [[tutorial]] page for more details about specifying superoperators within QETLAB).
	* <tt>DIM</tt> (optional, default has input and output spaces of equal dimension): A 1-by-2 vector containing the input and output dimensions of <tt>PHI</tt>, in that order (equivalently, these are the dimensions of the first and second subsystems of the Choi matrix <tt>PHI</tt>, in that order). If the input or output space is not square, then <tt>DIM</tt>'s first row should contain the input and output row dimensions, and its second row should contain its input and output column dimensions. <tt>DIM</tt> is required if and only if <tt>PHI</tt> has unequal input and output dimensions and is provided as a Choi matrix.		* <tt>DIM</tt> (optional, default has input and output spaces of equal dimension): A 1-by-2 vector containing the input and output dimensions of <tt>PHI</tt>, in that order (equivalently, these are the dimensions of the first and second subsystems of the Choi matrix <tt>PHI</tt>, in that order). If the input or output space is not square, then <tt>DIM</tt>'s first row should contain the input and output row dimensions, and its second row should contain its input and output column dimensions. <tt>DIM</tt> is required if and only if <tt>PHI</tt> has unequal input and output dimensions and is provided as a Choi matrix.

	==Examples==		==Examples==
	===Relationship with the [[diamond norm]]===		===Relationship with the diamond norm===
	The CB norm of a superoperator $\Phi$ is equal to the [[diamond norm]] of the [[dual map]] $\Phi^\dagger$:		The CB norm of a superoperator $\Phi$ is equal to the diamond norm of the dual map $\Phi^\dagger$:
	<syntaxhighlight>		<syntaxhighlight>
	>> Phi = {[1 2;3 4],[0 1;1 0] ; [0 1;2 0],[1 1;1 1] ; [1 1;-1 3],[1 4;0 0]};		>> Phi = {[1 2;3 4],[0 1;1 0] ; [0 1;2 0],[1 1;1 1] ; [1 1;-1 3],[1 4;0 0]};
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	19.5928		19.5928
	</syntaxhighlight>		</syntaxhighlight>

			===Can be used in CVX===
			Just like the <tt>[[DiamondNorm]]</tt> function, <tt>CBNorm</tt> is a convex function that can be used within CVX optimization problems. See the [[DiamondNorm#Can_be_used_within_CVX\|example on the <tt>DiamondNorm</tt> documentation page]].

	{{SourceCode\|name=CBNorm}}		{{SourceCode\|name=CBNorm}}

Nathaniel at 16:27, 22 September 2014

2014-09-22T16:27:52Z

← Older revision		Revision as of 16:27, 22 September 2014
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	\|name=CBNorm		\|name=CBNorm
	\|desc=Computes the [[completely bounded norm]] of a superoperator		\|desc=Computes the [[completely bounded norm]] of a superoperator
			\|req=[http://cvxr.com/cvx/ cvx]
	\|rel=[[DiamondNorm]]		\|rel=[[DiamondNorm]]
			\|cat=[[List of functions#Norms\|Norms]]
	\|upd=January 22, 2013		\|upd=January 22, 2013
	\|v=1.00}}		\|v=0.50}}
	<tt>'''CBNorm'''</tt> is a [[List of functions\|function]] that computes the [[completely bounded norm\|completely bounded (CB) norm]] $\\|\Phi\\|_{cb}$ of a superoperator $\Phi$.		<tt>'''CBNorm'''</tt> is a [[List of functions\|function]] that computes the [[completely bounded norm\|completely bounded (CB) norm]] $\\|\Phi\\|_{cb}$ of a superoperator $\Phi$.

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	==Argument descriptions==		==Argument descriptions==
	* <tt>PHI</tt>: A superoperator. Should be provided as either a [[Choi matrix]], or as a cell with either 1 or 2 columns (see the [[tutorial]] page for more details about specifying superoperators within QETLAB)~~. <tt>PHIC</tt> will be a cell of Kraus operators if <tt>PHI</tt> is a cell of Kraus operators, and similarly <tt>PHIC</tt> will be a Choi matrix if <tt>PHI</tt> is a Choi matrix~~.		* <tt>PHI</tt>: A superoperator. Should be provided as either a [[Choi matrix]], or as a cell with either 1 or 2 columns (see the [[tutorial]] page for more details about specifying superoperators within QETLAB).
	* <tt>DIM</tt> (optional, default has input and output spaces of equal dimension): A 1-by-2 vector containing the input and output dimensions of <tt>PHI</tt>, in that order (equivalently, these are the dimensions of the first and second subsystems of the Choi matrix <tt>PHI</tt>, in that order). If the input or output space is not square, then <tt>DIM</tt>'s first row should contain the input and output row dimensions, and its second row should contain its input and output column dimensions. <tt>DIM</tt> is required if and only if <tt>PHI</tt> has unequal input and output dimensions and is provided as a Choi matrix.		* <tt>DIM</tt> (optional, default has input and output spaces of equal dimension): A 1-by-2 vector containing the input and output dimensions of <tt>PHI</tt>, in that order (equivalently, these are the dimensions of the first and second subsystems of the Choi matrix <tt>PHI</tt>, in that order). If the input or output space is not square, then <tt>DIM</tt>'s first row should contain the input and output row dimensions, and its second row should contain its input and output column dimensions. <tt>DIM</tt> is required if and only if <tt>PHI</tt> has unequal input and output dimensions and is provided as a Choi matrix.

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	===Relationship with the [[diamond norm]]===		===Relationship with the [[diamond norm]]===
	The CB norm of a superoperator $\Phi$ is equal to the [[diamond norm]] of the [[dual map]] $\Phi^\dagger$:		The CB norm of a superoperator $\Phi$ is equal to the [[diamond norm]] of the [[dual map]] $\Phi^\dagger$:
	<~~pre<noinclude></noinclude>~~>		<syntaxhighlight>
	>> Phi = {[1 2;3 4],[0 1;1 0] ; [0 1;2 0],[1 1;1 1] ; [1 1;-1 3],[1 4;0 0]};		>> Phi = {[1 2;3 4],[0 1;1 0] ; [0 1;2 0],[1 1;1 1] ; [1 1;-1 3],[1 4;0 0]};
	>> CBNorm(Phi)		>> CBNorm(Phi)
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	19.5928		19.5928

	>> [[DiamondNorm]](~~[[DualMap\|~~DualMap(Phi)]])		>> DiamondNorm(DualMap(Phi))

	ans =		ans =

	19.5928		19.5928
	</~~pre<noinclude></noinclude>~~>		</syntaxhighlight>

			{{SourceCode\|name=CBNorm}}

Nathaniel: Created page with "{{Function |name=CBNorm |desc=Computes the completely bounded norm of a superoperator |rel=DiamondNorm |upd=January 22, 2013 |v=1.00}} `'''CBNorm'''` is a [[Lis..."

2013-01-22T21:25:03Z

Created page with "{{Function |name=CBNorm |desc=Computes the completely bounded norm of a superoperator |rel=DiamondNorm |upd=January 22, 2013 |v=1.00}} <tt>'''CBNorm'''</tt> is a [[Lis..."

New page

{{Function
|name=CBNorm
|desc=Computes the [[completely bounded norm]] of a superoperator
|rel=[[DiamondNorm]]
|upd=January 22, 2013
|v=1.00}}
<tt>'''CBNorm'''</tt> is a [[List of functions|function]] that computes the [[completely bounded norm|completely bounded (CB) norm]] $\|\Phi\|_{cb}$ of a superoperator $\Phi$.

==Syntax==
* <tt>CB = CBNorm(PHI)</tt>
* <tt>CB = CBNorm(PHI,DIM)</tt>

==Argument descriptions==
* <tt>PHI</tt>: A superoperator. Should be provided as either a [[Choi matrix]], or as a cell with either 1 or 2 columns (see the [[tutorial]] page for more details about specifying superoperators within QETLAB). <tt>PHIC</tt> will be a cell of Kraus operators if <tt>PHI</tt> is a cell of Kraus operators, and similarly <tt>PHIC</tt> will be a Choi matrix if <tt>PHI</tt> is a Choi matrix.
* <tt>DIM</tt> (optional, default has input and output spaces of equal dimension): A 1-by-2 vector containing the input and output dimensions of <tt>PHI</tt>, in that order (equivalently, these are the dimensions of the first and second subsystems of the Choi matrix <tt>PHI</tt>, in that order). If the input or output space is not square, then <tt>DIM</tt>'s first row should contain the input and output row dimensions, and its second row should contain its input and output column dimensions. <tt>DIM</tt> is required if and only if <tt>PHI</tt> has unequal input and output dimensions and is provided as a Choi matrix.

==Examples==
===Relationship with the [[diamond norm]]===
The CB norm of a superoperator $\Phi$ is equal to the [[diamond norm]] of the [[dual map]] $\Phi^\dagger$:
<pre<noinclude></noinclude>>
>> Phi = {[1 2;3 4],[0 1;1 0] ; [0 1;2 0],[1 1;1 1] ; [1 1;-1 3],[1 4;0 0]};
>> CBNorm(Phi)

ans =

19.5928

>> [[DiamondNorm]]([[DualMap|DualMap(Phi)]])

ans =

19.5928
</pre<noinclude></noinclude>>