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) $M_iin U(2)$?










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    up vote
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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) $M_iin U(2)$?










    share|cite|improve this question
























      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) $M_iin U(2)$?










      share|cite|improve this question













      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






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      asked Nov 13 at 13:58









      user2820579

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