Purity - Revision history

Nathaniel at 01:40, 13 May 2018

2018-05-13T01:40:07Z

← Older revision		Revision as of 01:40, 13 May 2018
Line 5:		Line 5:
	\|upd=October 15, 2014		\|upd=October 15, 2014
	\|v=0.50}}		\|v=0.50}}
	<tt>'''Purity'''</tt> is a [[List of functions\|function]] that computes the purity of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$.		<tt>'''Purity'''</tt> is a [[List of functions\|function]] that computes the purity of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$).

	==Syntax==		==Syntax==

Nathaniel at 13:34, 24 June 2015

2015-06-24T13:34:15Z

← Older revision		Revision as of 13:34, 24 June 2015
Line 5:		Line 5:
	\|upd=October 15, 2014		\|upd=October 15, 2014
	\|v=0.50}}		\|v=0.50}}
	<tt>'''Purity'''</tt> is a [[List of functions\|function]] that computes the ~~[[purity_(concept)\|~~purity]] of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$.		<tt>'''Purity'''</tt> is a [[List of functions\|function]] that computes the purity of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$.

	==Syntax==		==Syntax==

Nathaniel at 13:57, 15 October 2014

2014-10-15T13:57:32Z

← Older revision		Revision as of 13:57, 15 October 2014
Line 3:		Line 3:
	\|desc=Computes the purity of a quantum state		\|desc=Computes the purity of a quantum state
	\|cat=[[List of functions#Miscellaneous\|Miscellaneous]]		\|cat=[[List of functions#Miscellaneous\|Miscellaneous]]
	\|upd=~~July 18~~, ~~2013~~		\|upd=October 15, 2014
	\|v=1.00}}		\|v=0.50}}
	<tt>'''Purity'''</tt> is a [[List of functions\|function]] that computes the [[purity_(concept)\|purity]] of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$.		<tt>'''Purity'''</tt> is a [[List of functions\|function]] that computes the [[purity_(concept)\|purity]] of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$.

Nathaniel at 15:46, 29 September 2014

2014-09-29T15:46:58Z

← Older revision		Revision as of 15:46, 29 September 2014
Line 2:		Line 2:
	\|name=Purity		\|name=Purity
	\|desc=Computes the purity of a quantum state		\|desc=Computes the purity of a quantum state
			\|cat=[[List of functions#Miscellaneous\|Miscellaneous]]
	\|upd=July 18, 2013		\|upd=July 18, 2013
	\|v=1.00}}		\|v=1.00}}
Line 15:		Line 16:
	===Purity of pure states===		===Purity of pure states===
	Pure states have purity equal to 1, as illustrated by the following code:		Pure states have purity equal to 1, as illustrated by the following code:
	<~~pre<noinclude></noinclude>~~>		<syntaxhighlight>
	>> phi = ~~[[RandomStateVector\|~~RandomStateVector(3)]];		>> phi = RandomStateVector(3);
	>> Purity(phi*phi')		>> Purity(phi*phi')

Line 23:		Line 24:
	1.0000		1.0000

	>> Purity(~~[[RandomDensityMatrix\|~~RandomDensityMatrix(3,0,1)]])		>> Purity(RandomDensityMatrix(3,0,1))

	ans =		ans =

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

	===Purity of mixed states===		===Purity of mixed states===
	If $\rho \in M_d$ is mixed then its purity is strictly less than 1. Its purity attains its minimum value of $1/d$ if and only if $\rho$ is the maximally-mixed state (i.e., the scaled identity operator).		If $\rho \in M_d$ is mixed then its purity is strictly less than 1. Its purity attains its minimum value of $1/d$ if and only if $\rho$ is the maximally-mixed state (i.e., the scaled identity operator).
	<~~pre<noinclude></noinclude>~~>		<syntaxhighlight>
	>> Purity(~~[[WernerState\|~~WernerState(2,1/4)]]) % the state WernerState(2,1/4) acts on 4-dimensional space		>> Purity(WernerState(2,1/4)) % the state WernerState(2,1/4) acts on 4-dimensional space

	ans =		ans =
Line 44:		Line 45:

	0.2500		0.2500
	</~~pre<noinclude></noinclude>~~>		</syntaxhighlight>

			{{SourceCode\|name=Purity}}

Nathaniel: Created page with "{{Function |name=Purity |desc=Computes the purity of a quantum state |upd=July 18, 2013 |v=1.00}} `'''Purity'''` is a function that computes the [..."

2013-07-18T21:58:50Z

Created page with "{{Function |name=Purity |desc=Computes the purity of a quantum state |upd=July 18, 2013 |v=1.00}} <tt>'''Purity'''</tt> is a function that computes the [..."

New page

{{Function
|name=Purity
|desc=Computes the purity of a quantum state
|upd=July 18, 2013
|v=1.00}}
<tt>'''Purity'''</tt> is a [[List of functions|function]] that computes the [[purity_(concept)|purity]] of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$.

==Syntax==
* <tt>GAMMA = Purity(RHO)</tt>

==Argument descriptions==
* <tt>RHO</tt>: A density matrix to have its purity computed.

==Examples==
===Purity of pure states===
Pure states have purity equal to 1, as illustrated by the following code:
<pre<noinclude></noinclude>>
>> phi = [[RandomStateVector|RandomStateVector(3)]];
>> Purity(phi*phi')

ans =

1.0000

>> Purity([[RandomDensityMatrix|RandomDensityMatrix(3,0,1)]])

ans =

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

===Purity of mixed states===
If $\rho \in M_d$ is mixed then its purity is strictly less than 1. Its purity attains its minimum value of $1/d$ if and only if $\rho$ is the maximally-mixed state (i.e., the scaled identity operator).
<pre<noinclude></noinclude>>
>> Purity([[WernerState|WernerState(2,1/4)]]) % the state WernerState(2,1/4) acts on 4-dimensional space

ans =

0.2653

>> Purity(eye(4)/4)

ans =

0.2500
</pre<noinclude></noinclude>>

Purity - Revision history

Nathaniel at 01:40, 13 May 2018

Nathaniel at 13:34, 24 June 2015

Nathaniel at 13:57, 15 October 2014

Nathaniel at 15:46, 29 September 2014

Nathaniel: Created page with "{{Function |name=Purity |desc=Computes the purity of a quantum state |upd=July 18, 2013 |v=1.00}} '''Purity''' is a function that computes the [..."

Nathaniel: Created page with "{{Function |name=Purity |desc=Computes the purity of a quantum state |upd=July 18, 2013 |v=1.00}} `'''Purity'''` is a function that computes the [..."