Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
QuantumMeasurementOperator  |
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Details and Options
Examples
(15)
Basic Examples
(8)
In[1]:=
 | QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
 |  |
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In[1]:=
| QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
|  |
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One can measure an observable by inputting its matrix:
In[1]:=
qmo=
[PauliMatrix[2]]
 | QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
|  |
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In[2]:=
m=qmo
1+,+
 | QuantumState |
2
1
2
Out[2]=
QuantumMeasurement
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Probability plot of measurement results:
In[3]:=
m["ProbabilityPlot"]
Out[3]=
Post-measurement states:
In[4]:=
#["Formula"]&/@m["StateAssociation"]//Map@Simplify
Out[4]=
0(-1-(+
1
2
2
)0+(+2
)1,11
2
2
)0+(1+2
)1
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
|  |
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In[2]:=
qmo=
[ψ0["Dimensions"]]
| QuantumMeasurementOperator |
| QuantumBasis |
Out[2]=
QuantumMeasurementOperator
|  |
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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
|  |
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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 the 1st qudit):
In[1]:=
qmo=
["ComputationalBasis",{2}]
| QuantumMeasurementOperator |
Out[1]=
QuantumMeasurementOperator
|  |
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In[2]:=
qmo
[{"UniformSuperposition",2}]["StateAmplitudes"]
| QuantumState |
Out[2]=
000,010,10,110,1000,01,100,11
1
2
1
2
1
2
1
2
Define measurement operator by a QuantumBasis object (as an eigenbasis) and a list of eigenvalues:
In[1]:=
qmo=
["Bell"{1,2,3,4}]
| QuantumMeasurementOperator |
Test each element of POVM is explicitly positive semi-definite:
Test the complete relation of POVM elements:
Define the quantum measurement using POVM: