added 38 characters in body; edited tags
Source Link
Sanchayan Dutta
  • 15.5k
  • 5
  • 39
  • 91

Wikipedia saysNielsen and Chuang (on page 188 exercise 4.33) says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how.

enter image description here

The matrix representing the circuit functionality is:

$$\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 \\ 0 & 1 &-1 & 0 \end{bmatrix}$$

Now, what I have found out is, that instead of measuring in the Bell state, it is actually simply converting $|00\rangle$ to $\beta_{00}$, $|01\rangle$ to $\beta_{01}$ and vice versa and so on. So it's actually transforming from one basis to another. But how is it a measurement in the Bell state?

Suppose you take the vector $(1,0,0,0)$ in the Bell state it's written $(1,0,1,0)$ then when measuring in Bell state I would expect you get either $(1,0,0,0)$ which is $|00\rangle + |11\rangle$ or $(0,0,1,0)$ which is $|00\rangle-|11\rangle$. But why isn't it doing the measurement but just converting from basis to basis and yet Wikipedia says it's a measurement?

Wikipedia says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how.

enter image description here

The matrix representing the circuit functionality is:

$$\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 \\ 0 & 1 &-1 & 0 \end{bmatrix}$$

Now, what I have found out is, that instead of measuring in the Bell state, it is actually simply converting $|00\rangle$ to $\beta_{00}$, $|01\rangle$ to $\beta_{01}$ and vice versa and so on. So it's actually transforming from one basis to another. But how is it a measurement in the Bell state?

Suppose you take the vector $(1,0,0,0)$ in the Bell state it's written $(1,0,1,0)$ then when measuring in Bell state I would expect you get either $(1,0,0,0)$ which is $|00\rangle + |11\rangle$ or $(0,0,1,0)$ which is $|00\rangle-|11\rangle$. But why isn't it doing the measurement but just converting from basis to basis and yet Wikipedia says it's a measurement?

Nielsen and Chuang (on page 188 exercise 4.33) says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how.

enter image description here

The matrix representing the circuit functionality is:

$$\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 \\ 0 & 1 &-1 & 0 \end{bmatrix}$$

Now, what I have found out is, that instead of measuring in the Bell state, it is actually simply converting $|00\rangle$ to $\beta_{00}$, $|01\rangle$ to $\beta_{01}$ and vice versa and so on. So it's actually transforming from one basis to another. But how is it a measurement in the Bell state?

Suppose you take the vector $(1,0,0,0)$ in the Bell state it's written $(1,0,1,0)$ then when measuring in Bell state I would expect you get either $(1,0,0,0)$ which is $|00\rangle + |11\rangle$ or $(0,0,1,0)$ which is $|00\rangle-|11\rangle$. But why isn't it doing the measurement but just converting from basis to basis and yet Wikipedia says it's a measurement?

added 91 characters in body
Source Link
Sanchayan Dutta
  • 15.5k
  • 5
  • 39
  • 91

Wikipedia says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how.

enter image description here

The matrix representing the circuit functionality is:

$$\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 \\ 0 & 1 &-1 & 0 \end{bmatrix}$$

Now, what I have found out is, that instead of measuring in the Bell state, it is actually simply converting $|00\rangle$ to $\beta_{00}$, $|01\rangle$ to $\beta_{01}$ and vice versa and so on. So it's actually transforming from one basis to another. But how is it a measurement in the Bell state?

Suppose you take the vector $(1,0,0,0)$ in the Bell state it's written $(1,0,1,0)$ then when measuring in Bell state I would expect you get either $(1,0,0,0)$ which is $|00\rangle + |11\rangle$ or $(0,0,1,0)$ which is $|00\rangle-|11\rangle$. But why isn't it doing the measurement but just converting from basis to basis and yet Wikipedia says it's a measurement?

Wikipedia says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how.

The matrix representing the circuit functionality is:

$$\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 \\ 0 & 1 &-1 & 0 \end{bmatrix}$$

Now, what I have found out is, that instead of measuring in the Bell state, it is actually simply converting $|00\rangle$ to $\beta_{00}$, $|01\rangle$ to $\beta_{01}$ and vice versa and so on. So it's actually transforming from one basis to another. But how is it a measurement in the Bell state?

Suppose you take the vector $(1,0,0,0)$ in the Bell state it's written $(1,0,1,0)$ then when measuring in Bell state I would expect you get either $(1,0,0,0)$ which is $|00\rangle + |11\rangle$ or $(0,0,1,0)$ which is $|00\rangle-|11\rangle$. But why isn't it doing the measurement but just converting from basis to basis and yet Wikipedia says it's a measurement?

Wikipedia says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how.

enter image description here

The matrix representing the circuit functionality is:

$$\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 \\ 0 & 1 &-1 & 0 \end{bmatrix}$$

Now, what I have found out is, that instead of measuring in the Bell state, it is actually simply converting $|00\rangle$ to $\beta_{00}$, $|01\rangle$ to $\beta_{01}$ and vice versa and so on. So it's actually transforming from one basis to another. But how is it a measurement in the Bell state?

Suppose you take the vector $(1,0,0,0)$ in the Bell state it's written $(1,0,1,0)$ then when measuring in Bell state I would expect you get either $(1,0,0,0)$ which is $|00\rangle + |11\rangle$ or $(0,0,1,0)$ which is $|00\rangle-|11\rangle$. But why isn't it doing the measurement but just converting from basis to basis and yet Wikipedia says it's a measurement?

Wikipedia says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how.

The matrix representing the circuit functionality is:

$$\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 \\ 0 & 1 &-1 & 0 \end{bmatrix}$$

Now, what I have found out is, that instead of measuring in the Bell state, it is actually simply converting $|00\rangle$ to B00$\beta_{00}$, $|01\rangle$ to B01$\beta_{01}$ and vice versa and so on. So it's actually transforming from one basis to another. But how is it a measurement in the Bell state?

Suppose you take the vector $(1,0,0,0)$ in the Bell state it's written $(1,0,1,0)$ then when measuring in Bell state I would expect you get either $(1,0,0,0)$ which is $|00\rangle + |11\rangle$ or $(0,0,1,0)$ which is $|00\rangle-|11\rangle$. But why isn't it doing the measurement but just converting from basis to basis and yet Wikipedia says it's a measurement?

Wikipedia says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how.

The matrix representing the circuit functionality is:

$$\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 \\ 0 & 1 &-1 & 0 \end{bmatrix}$$

Now, what I have found out is, that instead of measuring in the Bell state, it is actually simply converting $|00\rangle$ to B00, $|01\rangle$ to B01 and vice versa and so on. So it's actually transforming from one basis to another. But how is it a measurement in the Bell state?

Suppose you take the vector $(1,0,0,0)$ in the Bell state it's written $(1,0,1,0)$ then when measuring in Bell state I would expect you get either $(1,0,0,0)$ which is $|00\rangle + |11\rangle$ or $(0,0,1,0)$ which is $|00\rangle-|11\rangle$. But why isn't it doing the measurement but just converting from basis to basis and yet Wikipedia says it's a measurement?

Wikipedia says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how.

The matrix representing the circuit functionality is:

$$\begin{bmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 \\ 0 & 1 &-1 & 0 \end{bmatrix}$$

Now, what I have found out is, that instead of measuring in the Bell state, it is actually simply converting $|00\rangle$ to $\beta_{00}$, $|01\rangle$ to $\beta_{01}$ and vice versa and so on. So it's actually transforming from one basis to another. But how is it a measurement in the Bell state?

Suppose you take the vector $(1,0,0,0)$ in the Bell state it's written $(1,0,1,0)$ then when measuring in Bell state I would expect you get either $(1,0,0,0)$ which is $|00\rangle + |11\rangle$ or $(0,0,1,0)$ which is $|00\rangle-|11\rangle$. But why isn't it doing the measurement but just converting from basis to basis and yet Wikipedia says it's a measurement?

deleted 25 characters in body
Source Link
Sanchayan Dutta
  • 15.5k
  • 5
  • 39
  • 91
Loading
added 121 characters in body
Source Link
Sanchayan Dutta
  • 15.5k
  • 5
  • 39
  • 91
Loading
Source Link
bilanush
  • 793
  • 4
  • 8
Loading