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Kraus
.
Stinespring100
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Imports
Init
Kraus.Basic
Kraus.Stinespring
Mathlib.Analysis.Matrix.Order
Mathlib.Analysis.RCLike.Basic
Imported by
stinespringForm_eq
heisenberg_schrõdinger_picture
tr₂_one_of_unital
Stinespring dilation
#
source
theorem
stinespringForm_eq
{
R
:
Type
u_1}
[
RCLike
R
]
{
m
r
:
ℕ
}
(
K
:
Fin
r
→
Matrix
(
Fin
m
)
(
Fin
m
)
R
)
(
ρ
:
Matrix
(
Fin
m
)
(
Fin
m
)
R
)
:
tr₂
(
stinespringDilation
K
ρ
)
=
krausApply
K
ρ
A version of the Stinespring Dilation Theorem.
source
theorem
heisenberg_schrõdinger_picture
{
m
r
:
ℕ
}
(
K
:
Fin
r
.
succ
→
Matrix
(
Fin
m
)
(
Fin
m
)
ℂ
)
(
ρ
:
Matrix
(
Fin
m
)
(
Fin
m
)
ℂ
)
:
0
=
0
source
theorem
tr₂_one_of_unital
{
m
r
:
ℕ
}
(
K
:
Fin
r
→
Matrix
(
Fin
m
)
(
Fin
m
)
ℂ
)
(
hu
:
unital
K
)
:
tr₂
(
stinespringOp
K
*
(
stinespringOp
K
)
.
conjTranspose
)
=
1