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Entangled states

  1. Nov 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose we define states [0] and [1] be the basis which [0] = (1,0) and [1] = (0,1).

    There are two things I want to ask. Are the following states product or entangled states?

    (i) [Xi] = \frac{1}{2} ([00] + [01] + [10] - [11])

    (ii) [Xi] = \frac{1}{\sqrt{10}} ([01] + 3 [10])

    2. Relevant equations



    3. The attempt at a solution

    I understand that [Xi] = \frac{1}{2} ([00] + [01] + [10] + [11]) is a product state, since it can be represented by the tensor products between two qubits. But I just can't see what the answers are for the questions I stated at above. Hm... I guess they're both entangled, am I wrong?
     
  2. jcsd
  3. Nov 4, 2009 #2

    gabbagabbahey

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    A general two qubit product state is [itex]|\Psi\rangle=(\alpha|0\rangle+\beta|1\rangle)\otimes(\gamma|0\rangle+\delta|1\rangle)[/itex]....Expand the tensor product and equate it to the state you wish to test... are there any values of [itex]\alpha[/itex], [itex]\beta[/itex], [itex]\gamma[/itex] and [itex]\delta[/itex] that make that equality hold?
     
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