How to find if an operator is the tensor product of more lower dimensional operators.
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In quantum computation and quantum information it is very common to use e.g. the effect of a Hadamard matrix $H$ over $2n$ spins. Using (I think it is called the Kroenecker product in mathematical literature) the tensor product $otimes$, one can write the Hadamard matrix for example for two spins as
$$
Hotimes H.
$$
I want to ask precisely the opposite question. Is there a theorem(s) that ensures that, e.g. $Min U(4)$ could be written as
$$
M = M_1otimes M_2,
$$
where (perhaps) $M_iin U(2)$?
abstract-algebra quantum-computation
asked Nov 13 at 13:58
user2820579
703412
add a comment |
up vote
2
down vote
favorite
In quantum computation and quantum information it is very common to use e.g. the effect of a Hadamard matrix $H$ over $2n$ spins. Using (I think it is called the Kroenecker product in mathematical literature) the tensor product $otimes$, one can write the Hadamard matrix for example for two spins as
$$
Hotimes H.
$$
I want to ask precisely the opposite question. Is there a theorem(s) that ensures that, e.g. $Min U(4)$ could be written as
$$
M = M_1otimes M_2,
$$
where (perhaps) $M_iin U(2)$?
abstract-algebra quantum-computation
asked Nov 13 at 13:58
user2820579
703412
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
In quantum computation and quantum information it is very common to use e.g. the effect of a Hadamard matrix $H$ over $2n$ spins. Using (I think it is called the Kroenecker product in mathematical literature) the tensor product $otimes$, one can write the Hadamard matrix for example for two spins as
$$
Hotimes H.
$$
I want to ask precisely the opposite question. Is there a theorem(s) that ensures that, e.g. $Min U(4)$ could be written as
$$
M = M_1otimes M_2,
$$
where (perhaps) $M_iin U(2)$?
abstract-algebra quantum-computation
asked Nov 13 at 13:58
user2820579
703412
In quantum computation and quantum information it is very common to use e.g. the effect of a Hadamard matrix $H$ over $2n$ spins. Using (I think it is called the Kroenecker product in mathematical literature) the tensor product $otimes$, one can write the Hadamard matrix for example for two spins as
$$
Hotimes H.
$$
I want to ask precisely the opposite question. Is there a theorem(s) that ensures that, e.g. $Min U(4)$ could be written as
$$
M = M_1otimes M_2,
$$
where (perhaps) $M_iin U(2)$?
abstract-algebra quantum-computation
abstract-algebra quantum-computation
asked Nov 13 at 13:58
user2820579
703412
asked Nov 13 at 13:58
user2820579
703412
asked Nov 13 at 13:58
user2820579
703412
asked Nov 13 at 13:58
user2820579
703412
asked Nov 13 at 13:58
user2820579
703412
703412
add a comment |
add a comment |
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