Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
QuantumMeasurementOperator  |
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Details and Options
Examples
(11)
Basic Examples
(6)
In[1]:=
 | QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
 |  |
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In[1]:=
| QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
 |  |
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Corresponding spectral representation:
In[2]:=
%["Operator"]//TraditionalForm
Out[2]//TraditionalForm=
2|〉〈|+3|〉〈|-|〉〈|+4|〉〈|
+
Φ
+
Φ
-
Φ
-
Φ
+
Ψ
+
Ψ
-
Ψ
-
Ψ
A measurement can be specified by inputting only the corresponding basis. For example, consider a quantum state in 3D:
In[1]:=
ψ=
["RandomPure",3]
 | QuantumState |
Out[1]=
QuantumState
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Define the measurement operator, given the basis of the state
In[2]:=
qmo=
[ψ["Basis"]]
| QuantumMeasurementOperator |
Out[2]=
QuantumMeasurementOperator
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Generate the corresponding measurement object, by applying the measurement operator on the state:
In[3]:=
m=qmo[ψ];m["ProbabilityPlot"]
Out[3]=
A measurement can be defined in the computational basis for any number of qudits. Define the measurement operator of two qubits:
In[1]:=
qmo=
[{1,2}]
| QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
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Measure qubits in the computational basis, given a random state:
In[2]:=
m=qmo
[{"RandomPure",2}];m["ProbabilityPlot"]
 | QuantumState |
Out[2]=
A one-qudit measurement operator can act on system of many qudits.
In[1]:=
qmo=
[{2}]
| QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
|  |
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In[2]:=
mea=qmo
[{"RandomPure",2}];mea["ProbabilityPlot"]
| QuantumState |
Out[2]=
One can also input any set of operators, with and =, to generalize measurements as positive operator-valued measures (POVMs):
{}
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:
In[3]:=
(Plus@@povm)IdentityMatrix[2]
Out[3]=
True
Define the quantum measurement using POVM:
In[4]:=
qmo=
[povm]
| QuantumMeasurementOperator |
Out[4]=
QuantumMeasurementOperator
|  |
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In[5]:=
qmo
[{1,1}]["ProbabilityPlot"]
 | QuantumState |
Out[5]=
