In[]:=
PacletInstall[CloudObject["https://wolfr.am/DevWQCF"],​​ForceVersionInstallTrue]
Out[]=
PacletObject
Name: Wolfram/QuantumFramework
Version: 1.0.24

In[]:=
​​<<Wolfram`QuantumFramework`
​
​How I understand Werner's quantum state
In[]:=
​​p=0.3;​​phi=QuantumState["PhiPlus"];​​A=QuantumState[{{1/2,0},{0,1/2}}];​​B=QuantumState[{{1/2,0},{0,1/2}}];​​AB=QuantumState[{{1/4,0,0,0},{0,1/4,0,0},{0,0,1/4,0},{0,​​0,0,1/4}}];​​Wer=QuantumState[pphi["DensityMatrix"]+(1-p)AB["DensityMatrix"]]​​Wer["Formula"]​​Wer["DensityMatrix"]//Normal//MatrixForm​​QuantumEntangledQ[Wer]
Out[]=
QuantumState
Mixed state
Qudits: 2
Type: Matrix
Dimension: 4
Picture: Schrödinger
​

Out[]=
0.325|0000〉+0.15|0011〉+0.175|0101〉+0.175|1010〉+0.15|1100〉+0.325|1111〉
Out[]//MatrixForm=
0.325
0.
0.
0.15
0.
0.175
0.
0.
0.
0.
0.175
0.
0.15
0.
0.
0.325
Out[]=
False
I cannot see how to get the same result for the built in formula where Werner states with p>=1/2 are not entangled, while p<1/2 are:​
​(my method uses 1/3< p<=1 are entangled )
In[]:=
​​QuantumState[{"Werner",1/3,2}]​​%["Formula"]​​QuantumEntangledQ[%%]​​
Out[]=
QuantumState
Mixed state
Qudits: 2
Type: Matrix
Dimension: 4
Picture: Schrödinger
​

Out[]=
1
9
|0000〉+
7
18
|0101〉-
5
18
|0110〉-
5
18
|1001〉+
7
18
|1010〉+
1
9
|1111〉
Out[]=
True
In[]:=
​​QuantumState[{"Werner",1/3,2}]["DensityMatrix"]//Normal//MatrixForm
Out[]//MatrixForm=
1
9
0
0
0
0
7
18
-
5
18
0
0
-
5
18
7
18
0
0
0
0
1
9
In[]:=
​​psi=QuantumState[{α,β,γ,δ}];​​psi["DensityMatrix"]//Normal//MatrixForm​​psi["Transpose",{1}]["DensityMatrix"]//Normal//MatrixForm​​psi["Transpose",{2}]["DensityMatrix"]//Normal//MatrixForm
Out[]//MatrixForm=
αConjugate[α]
αConjugate[β]
αConjugate[γ]
αConjugate[δ]
βConjugate[α]
βConjugate[β]
βConjugate[γ]
βConjugate[δ]
γConjugate[α]
γConjugate[β]
γConjugate[γ]
γConjugate[δ]
δConjugate[α]
δConjugate[β]
δConjugate[γ]
δConjugate[δ]
Out[]//MatrixForm=
αConjugate[α]
αConjugate[β]
γConjugate[α]
γConjugate[β]
βConjugate[α]
βConjugate[β]
δConjugate[α]
δConjugate[β]
αConjugate[γ]
αConjugate[δ]
γConjugate[γ]
γConjugate[δ]
βConjugate[γ]
βConjugate[δ]
δConjugate[γ]
δConjugate[δ]
Out[]//MatrixForm=
αConjugate[α]
βConjugate[α]
αConjugate[γ]
βConjugate[γ]
αConjugate[β]
βConjugate[β]
αConjugate[δ]
βConjugate[δ]
γConjugate[α]
δConjugate[α]
γConjugate[γ]
δConjugate[γ]
γConjugate[β]
δConjugate[β]
γConjugate[δ]
δConjugate[δ]
In[]:=
​​QuantumPatrialTranspose[psi]
Out[]=
QuantumPatrialTransposeQuantumState
Pure state
Qudits: 2
Type: Vector
Dimension: 4
Picture: Schrödinger
​

​​