Wolfram Language Paclet Repository (Under Development)
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
QuantumMeasurementOperator  |  |
| QuantumMeasurementOperator[op,order,t,qb] op order t qb |
| QuantumMeasurementOperator[matrix,order,qb] matrix qb order |
| QuantumMeasurementOperator[basis->eig,order] QuantumBasis basis eig order |
| QuantumMeasurementOperator[qm,qb] QuantumMeasurementOperator qm qb |
Details
Examples
(14)
Basic Examples
(7)
Specify a by basis name:
QuantumMeasurementOperator
In[337]:=
 | QuantumMeasurementOperator |
Out[337]=
QuantumMeasurementOperator
 |  |
|
———
Specify a object given a basis with customized eigenvalues:
QuantumMeasurementOperator
In[1]:=
| QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
|  |
|
———
One can measure an observable by inputting its matrix:
In[1]:=
qmo=
[PauliMatrix[2]]
| QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
|  |
|
In[2]:=
m=qmo
1+,+
| QuantumState |
2
1
2
Out[2]=
QuantumMeasurement
|  |
|
Probability Plot of measurement results"
In[3]:=
m["ProbabilityPlot"]
Out[3]=
Post-measurement states"
In[4]:=
#["Formula"]&/@m["StateAssociation"]
Out[4]=
+,+
-1
|0〉
2
|1〉
2
1
|0〉
2
|1〉
2
———
A measurement can be specified by inputting only the corresponding basis. For example, let's measure a 3D-qudit system in the state basis:
3
|0〉+2
|1〉+5
|2〉In[1]:=
ψ0=
[Sqrt@{-3,2,5},3]
| QuantumState |
Out[1]=
QuantumState
|  |
|
In[2]:=
qmo=
[ψ0["Dimensions"]]
| QuantumMeasurementOperator |
| QuantumBasis |
Out[2]=
QuantumMeasurementOperator
|  |
|
In[3]:=
m=qmo[ψ0];m["ProbabilityPlot"]
Out[3]=
———
A measurement can be defined in the computational basis for any number of qudits. For example, define measurement of a two-qudit system in the computational basis:
3
|00〉+2
|01〉+|10〉+5
|11〉In[1]:=
qmo=
["Computational",{1,2}]
| QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
|  |
|
Note if not specified, the basis is by default the computational one:
In[2]:=
qmo==
[{1,2}]
| QuantumMeasurementOperator |
Out[2]=
True
In[3]:=
m=qmo
[Sqrt@{-3,2,-1,5}];m["ProbabilityPlot"]
| QuantumState |
Out[3]=
———
A one-qudit measurement operator can act on system of many qudits when the order (target qudit for measurement) is given (by default it will be 1at qudit).
In[1]:=
qmo=
["ComputationalBasis",{2}]
| QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
| |
|
In[2]:=
qmo
[{"UniformSuperposition",2}]["StateAmplitudes"]
| QuantumState |
Out[2]=
|0〉|00〉1,|01〉0,|10〉1,|11〉0,|1〉|00〉0,|01〉1,|10〉0,|11〉1
———
One can also input any set of operators, with and =, to generalize measurements as positive operator-valued measures (POVMs).
{}
E
m
∑=I
E
m
E
m
M
m
M
m
In[1]:=
povm=,0,{0,0},,,,,,-,-,;
2
3
1
6
1
2
3
1
2
3
1
2
1
6
1
2
3
1
2
3
1
2
Test each element of POVM is explicitly positive semi-definite:
In[2]:=
PositiveSemidefiniteMatrixQ/@povm
Out[2]=
{True,True,True}
Test the complete relation of POVM elements:
Define the quantum measurement using POVM: