1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper
    Gold Member

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook