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State Tomography?

  1. Oct 27, 2008 #1
    I don't know where this question belongs:

    Given many pairs of [tex]\left|\Psi\right>[/tex] and [tex]U\left|\Psi\right>[/tex], for some unitary U, is it possible to identify U without completely determining the two states independently? I mean what is the least possible number of pairs needed (to be x% certain), and is it less than simply determining the two states?
     
  2. jcsd
  3. Oct 28, 2008 #2
    Is there even enough information to determine a general U?
     
  4. Oct 30, 2008 #3
    Anyone?
     
  5. Nov 1, 2008 #4
    No, there's not enough info to determine U from what you propose: even if you know |psi> and U|\psi, you really know only one column vector of U, not the whole U (take |\psi> as your first basis vector in Hilbert space)
     
  6. Nov 1, 2008 #5
    But for a specific U, like a permutation?
     
  7. Nov 1, 2008 #6
    Same answer, you only learn one column of the matrix.
     
  8. Nov 1, 2008 #7
    What if [itex]\left|\Psi\right>[/itex] were a tensor state of n qubits?
     
  9. Nov 1, 2008 #8
    If the tensor product consists of many different qubit states, and if the big U is a tensor product of identical U_2s on each qubit, then of course you can learn everything about U_2.
     
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