Nathaniel at 13:23, 14 February 2019

2019-02-14T13:23:44Z

Nathaniel: Created page with "{{Function |name=RandomPOVM |desc=Generates a random POVM (positive-operator valued measure) |rel=RandomSuperoperator
RandomUnitary |cat=List of functions#Rando..."

2016-01-06T19:51:14Z

Created page with "{{Function |name=RandomPOVM |desc=Generates a random POVM (positive-operator valued measure) |rel=RandomSuperoperator<br />RandomUnitary |cat=List of functions#Rando..."

New page

{{Function
|name=RandomPOVM
|desc=Generates a random POVM (positive-operator valued measure)
|rel=[[RandomSuperoperator]]<br />[[RandomUnitary]]
|cat=[[List of functions#Random_things|Random things]]
|upd=January 6, 2016}}
<tt>'''RandomPOVM'''</tt> is a [[List of functions|function]] that generates a random [https://en.wikipedia.org/wiki/POVM POVM (positive-operator valued measure)] with a specified dimension and number of measurement outcomes.

==Syntax==
* <tt>P = RandomPOVM(DIM,OUTC)</tt>
* <tt>P = RandomPOVM(DIM,OUTC,RE)</tt>

==Argument descriptions==
* <tt>DIM</tt>: A scalar indicating the size of the POVM elements (i.e., each POVM element will have size <tt>DIM</tt>-by-<tt>DIM</tt>).
* <tt>OUTC</tt>: The number of POVM elements (i.e., the number of possible measurement outcomes).
* <tt>RE</tt> (optional, default 0): A flag (either 1 or 0) indicating that the entries of the POVM should or should not all be real.

==Examples==
The following code generates a random POVM on 4-dimensional space with 3 measurement outcomes:
<syntaxhighlight>
>> P = RandomPOVM(4,3);
>> celldisp(P) % display the POVM elements

P{1} =

0.3485 + 0.0000i 0.0512 + 0.0443i 0.0016 - 0.0853i -0.0861 + 0.0509i
0.0512 - 0.0443i 0.4188 + 0.0000i -0.1040 - 0.0067i -0.0271 - 0.0281i
0.0016 + 0.0853i -0.1040 + 0.0067i 0.3005 + 0.0000i -0.0853 - 0.0330i
-0.0861 - 0.0509i -0.0271 + 0.0281i -0.0853 + 0.0330i 0.3845

P{2} =

0.3658 + 0.0000i 0.0037 - 0.0577i 0.0351 + 0.0928i 0.0223 + 0.0511i
0.0037 + 0.0577i 0.2127 + 0.0000i 0.0961 + 0.0384i 0.0656 - 0.0671i
0.0351 - 0.0928i 0.0961 - 0.0384i 0.4426 + 0.0000i 0.0813 - 0.0791i
0.0223 - 0.0511i 0.0656 + 0.0671i 0.0813 + 0.0791i 0.4032 - 0.0000i

P{3} =

0.2857 + 0.0000i -0.0549 + 0.0135i -0.0367 - 0.0076i 0.0638 - 0.1020i
-0.0549 - 0.0135i 0.3685 + 0.0000i 0.0079 - 0.0317i -0.0385 + 0.0952i
-0.0367 + 0.0076i 0.0079 + 0.0317i 0.2569 + 0.0000i 0.0040 + 0.1121i
0.0638 + 0.1020i -0.0385 - 0.0952i 0.0040 - 0.1121i 0.2123 + 0.0000i
</syntaxhighlight>

It is straightforward to verify that these operators are positive semidefinite and sum to the identity (and thus form a valid POVM):
<syntaxhighlight>
>> IsPSD(P{1})

ans =

1

>> IsPSD(P{2})

ans =

1

>> IsPSD(P{3})

ans =

1

>> P{1} + P{2} + P{3}

ans =

1.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i
0.0000 - 0.0000i 1.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i
-0.0000 + 0.0000i -0.0000 - 0.0000i 1.0000 + 0.0000i 0.0000 - 0.0000i
-0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 + 0.0000i 1.0000 + 0.0000i
</syntaxhighlight>

{{SourceCode|name=RandomPOVM}}

@@ Line 73: / Line 73: @@
    -0.0000 + 0.0000i   0.0000 - 0.0000i   0.0000 + 0.0000i   1.0000 + 0.0000i
 </syntaxhighlight>
 {{SourceCode|name=RandomPOVM}}

RandomPOVM - Revision history

Nathaniel at 13:23, 14 February 2019

Nathaniel: Created page with "{{Function |name=RandomPOVM |desc=Generates a random POVM (positive-operator valued measure) |rel=RandomSuperoperatorRandomUnitary |cat=List of functions#Rando..."

Nathaniel: Created page with "{{Function |name=RandomPOVM |desc=Generates a random POVM (positive-operator valued measure) |rel=RandomSuperoperator
RandomUnitary |cat=List of functions#Rando..."