MaximumOutputFidelity - Revision history

Nathaniel at 13:30, 22 May 2018

2018-05-22T13:30:56Z

← Older revision		Revision as of 13:30, 22 May 2018
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	\|name=MaximumOutputFidelity		\|name=MaximumOutputFidelity
	\|desc=Computes the maximum output fidelity of two quantum channels		\|desc=Computes the maximum output fidelity of two quantum channels
			\|req=[http://cvxr.com/cvx/ CVX]
	\|rel=[[DiamondNorm]]<br />[[Fidelity]]		\|rel=[[DiamondNorm]]<br />[[Fidelity]]
	\|cat=[[List of functions#Norms_and_distance_measures\|Norms and distance measures]]		\|cat=[[List of functions#Norms_and_distance_measures\|Norms and distance measures]]

Nathaniel: added CVX parameter

2014-12-24T16:35:35Z

added CVX parameter

← Older revision		Revision as of 16:35, 24 December 2014
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	\|rel=[[DiamondNorm]]<br />[[Fidelity]]		\|rel=[[DiamondNorm]]<br />[[Fidelity]]
	\|cat=[[List of functions#Norms_and_distance_measures\|Norms and distance measures]]		\|cat=[[List of functions#Norms_and_distance_measures\|Norms and distance measures]]
	\|upd=November 24, 2014}}		\|upd=November 24, 2014
			\|cvx=no}}
	<tt>'''MaximumOutputFidelity'''</tt> is a [[List of functions\|function]] that computes the maximum output fidelity between two quantum channels $\Phi$ and $\Psi$, defined as follows:		<tt>'''MaximumOutputFidelity'''</tt> is a [[List of functions\|function]] that computes the maximum output fidelity between two quantum channels $\Phi$ and $\Psi$, defined as follows:
	: <math>F_{max}(\Phi,\Psi) := \max_{\rho,\sigma}\big\{F(\Phi(\rho),\Psi(\sigma)) : \rho,\sigma \text{ are density matrices}\big\},</math>		: <math>F_{max}(\Phi,\Psi) := \max_{\rho,\sigma}\big\{F(\Phi(\rho),\Psi(\sigma)) : \rho,\sigma \text{ are density matrices}\big\},</math>

Nathaniel: Created page with "{{Function |name=MaximumOutputFidelity |desc=Computes the maximum output fidelity of two quantum channels |rel=DiamondNorm
Fidelity |cat=List of functions#Norms..."

2014-11-27T20:59:44Z

Created page with "{{Function |name=MaximumOutputFidelity |desc=Computes the maximum output fidelity of two quantum channels |rel=DiamondNorm<br />Fidelity |cat=List of functions#Norms..."

New page

{{Function
|name=MaximumOutputFidelity
|desc=Computes the maximum output fidelity of two quantum channels
|rel=[[DiamondNorm]]<br />[[Fidelity]]
|cat=[[List of functions#Norms_and_distance_measures|Norms and distance measures]]
|upd=November 24, 2014}}
<tt>'''MaximumOutputFidelity'''</tt> is a [[List of functions|function]] that computes the maximum output fidelity between two quantum channels $\Phi$ and $\Psi$, defined as follows:
: <math>F_{max}(\Phi,\Psi) := \max_{\rho,\sigma}\big\{F(\Phi(\rho),\Psi(\sigma)) : \rho,\sigma \text{ are density matrices}\big\},</math>
where $F(\cdot,\cdot)$ is the usual [[fidelity]] between quantum states.

==Syntax==
* <tt>MOF = MaximumOutputFidelity(PHI,PSI)</tt>
* <tt>MOF = MaximumOutputFidelity(PHI,PSI,DIM_PHI)</tt>
* <tt>MOF = MaximumOutputFidelity(PHI,PSI,DIM_PHI,DIM_PSI)</tt>

==Argument descriptions==
* <tt>PHI,PSI</tt>: Quantum channels, represented as either Choi matrices or cells of Kraus operators.
* <tt>DIM_PHI,DIM_PSI</tt> (optional): 1-by-2 vectors containing the input and output dimensions of <tt>PHI</tt> and <tt>PSI</tt>, respectively. These arguments must be provided if and only if <tt>PHI</tt> and <tt>PSI</tt> are provided as Choi matrices and they have unequal input and output dimensions.

==Examples==
The following code computes the minimum output fidelity of a random qutrit channel $\Psi$ with the identity channel:
<syntaxhighlight>
>> d = 3;
>> Phi = {eye(d)};
>> Psi = RandomSuperoperator(d);
>> MaximumOutputFidelity(Phi,Psi)

ans =

0.7638
</syntaxhighlight>

{{SourceCode|name=MaximumOutputFidelity}}

MaximumOutputFidelity - Revision history

Nathaniel at 13:30, 22 May 2018

Nathaniel: added CVX parameter

Nathaniel: Created page with "{{Function |name=MaximumOutputFidelity |desc=Computes the maximum output fidelity of two quantum channels |rel=DiamondNormFidelity |cat=List of functions#Norms..."

Nathaniel: Created page with "{{Function |name=MaximumOutputFidelity |desc=Computes the maximum output fidelity of two quantum channels |rel=DiamondNorm
Fidelity |cat=List of functions#Norms..."