Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
WickMutualInformation  |  |
|
| | ||||
| n×n grn anm | | ||||
| | |||||
| | |||||
Details and Options
Examples
(2)
Basic Examples
(1)
In[1]:=
$n=6;
In[2]:=
SeedRandom[356];
Construct a Wick state. Make sure that the state is normalized.
In[3]:=
ws=RandomWickState[$n]
Out[3]=
WickState
 |
|
In[4]:=
Norm[ws]
Out[4]=
1
Calculate the Green's functions.
In[5]:=
grn=WickGreenFunction[ws];grn//ArrayShort
Out[5]=
,
0.352675 | -0.124765+0.081456 | -0.0927493-0.157642 | 0.239447+0.00377437 | … |
-0.124765-0.081456 | 0.52844 | -0.0166767-0.161439 | 0.0610354+0.0451316 | … |
-0.0927493+0.157642 | -0.0166767+0.161439 | 0.774039 | -0.0588351-0.0562971 | … |
0.239447-0.00377437 | 0.0610354-0.0451316 | -0.0588351+0.0562971 | 0.617479 | … |
… | … | … | … | … |
0 | -0.102382+0.0567348 | -0.0768921-0.0707724 | -0.0893847-0.0740275 | … |
0.102382-0.0567348 | 0 | -0.00934571+0.180003 | 0.0708578+0.225105 | … |
0.0768921+0.0707724 | 0.00934571-0.180003 | 0 | 0.115353+0.0140258 | … |
0.0893847+0.0740275 | -0.0708578-0.225105 | -0.115353-0.0140258 | 0 | … |
… | … | … | … | … |
Consider a subsystem.
In[6]:=
aa=Range[$n/2]
Out[6]=
{1,2,3}
Calculate the mutual information between the subsystem and the rest.
In[7]:=
val=WickMutualInformation[grn,aa]
Out[7]=
3.39267
If you just need to calculate the mutual information once, there is a shortcut:
In[8]:=
WickMutualInformation[ws,aa]
Out[8]=
3.39267
Calculate the entanglement entropy between the subsystem and the rest.
In[9]:=
ent=WickEntanglementEntropy[grn,aa]
Out[9]=
1.69633
Since the Wick state is a pure state, the mutual information must be equal to twice the entropy of the subsystem.
In[10]:=
val-2*ent//Chop
Out[10]=
0
Scope
(1)
 |
|
 |
|
""