Quantum Computing problem [Quantum Teleportation] (Nelson and Chuang)

[maverick280857]

Hello

I am reading Nelson and Chuang's book on Quantum Computation. On pages 26-7 they describe quantum teleportation. I am facing essentially a math problem in going from the expression

$$\left|\psi_{2}\right> = \frac{1}{2}\left[\alpha(\left|0\right> + \left|1\right>)(\left|00\right> + \left|11\right>) + \beta(\left|0\right> - \left|1\right>)(\left|10\right> + \left|01\right>)\right]$$

to the expression

$$\left|\psi_{2}\right> = \frac{1}{2}\left[\left|00\right>(\alpha\left|0\right> + \beta\left|1\right>) + \left|01\right>(\alpha\left|1\right> + \beta\left|0\right>) + \left|10\right>(\alpha\left|0\right> - \beta\left|1\right>) + \left|11\right>(\alpha\left|1\right> - \beta\left|0\right>)\right\]$$

Would appreciate any help/suggestions to try to tackle this.

Thanks.

PS--It seems to be a regrouping of terms..I guess, but I still can't get it directly :P

 

[maverick280857]

got it...thanks

 

[sassan72]

Hello

I am reading Nelson and Chuang's book on Quantum Computation. On pages 26-7 they describe quantum teleportation. I am facing essentially a math problem in going from the expression

$$\left|\psi_{2}\right> = \frac{1}{2}\left[\alpha(\left|0\right> + \left|1\right>)(\left|00\right> + \left|11\right>) + \beta(\left|0\right> - \left|1\right>)(\left|10\right> + \left|01\right>)\right]$$

to the expression

$$\left|\psi_{2}\right> = \frac{1}{2}\left[\left|00\right>(\alpha\left|0\right> + \beta\left|1\right>) + \left|01\right>(\alpha\left|1\right> + \beta\left|0\right>) + \left|10\right>(\alpha\left|0\right> - \beta\left|1\right>) + \left|11\right>(\alpha\left|1\right> - \beta\left|0\right>)\right\]$$

Would appreciate any help/suggestions to try to tackle this.

Thanks.
hi
this relation is obtained by applying first single qubit Hadamard transformation on Alice's qubit and next two qubit CNOT transformation. you can refer to quantum computing by Mikio Nakahara, chapter 4,page 80, or C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W. K. Wootters, Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels, Phys. Rev. Lett. 70, 1895-1899 (1993)

 

[maverick280857]

hi
this relation is obtained by applying first single qubit Hadamard transformation on Alice's qubit and next two qubit CNOT transformation. you can refer to quantum computing by Mikio Nakahara, chapter 4,page 80, or C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W. K. Wootters, Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels, Phys. Rev. Lett. 70, 1895-1899 (1993)

Wow, been a long time..3 years. Thanks :-)