2 `\rangle` not `>`
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Not sure if I should ask this on CS or physics SE, but here goes.

I’m reading on quantum computing, and one thing that keeps confusing me is the following basic fact about QM:

Say we have a qbit A, and a qbit B, then two possible quantum states for $A$ are:

$$|+>=\frac {|0> + |1>}{\sqrt 2}$$$$|+\rangle=\frac {|0\rangle + |1\rangle}{\sqrt 2}$$

$$\frac {|00> + |11>}{\sqrt 2}$$$$\frac {|00\rangle + |11\rangle}{\sqrt 2}$$

In the first case, the qbit $A$ is in a quantum superposition between $0$ and $1$. In the second case, the qbits $A$ and $B$ are ALSO in a quantum superposition, but they are now entangled. I understand that there is a difference between these states, in the sense that the second is an entangled state, whereas the first one is not.

However, what I don’t understand, is why, solely from the perspective of $A$, there is a difference between these states. I read that in the second, entangled state, $A$ (taken as an individual qbit) is not in a superposition state, but in a mixed state. I know that this is a very important basic fact about QM but I still don’t really get it.

  • why is it not possible for $A$ to be both in an entangled state, AND in a superposition “with itself” (i.e. a pure state, rather than a mixed state). I.e. by what principle of quantum mechanics do we know this, and from what does this principle follow?

  • Is there an intuition behind this? I.e. how would quantum mechanics no longer make sense if it weren’t the case.

Not sure if I should ask this on CS or physics SE, but here goes.

I’m reading on quantum computing, and one thing that keeps confusing me is the following basic fact about QM:

Say we have a qbit A, and a qbit B, then two possible quantum states for $A$ are:

$$|+>=\frac {|0> + |1>}{\sqrt 2}$$

$$\frac {|00> + |11>}{\sqrt 2}$$

In the first case, the qbit $A$ is in a quantum superposition between $0$ and $1$. In the second case, the qbits $A$ and $B$ are ALSO in a quantum superposition, but they are now entangled. I understand that there is a difference between these states, in the sense that the second is an entangled state, whereas the first one is not.

However, what I don’t understand, is why, solely from the perspective of $A$, there is a difference between these states. I read that in the second, entangled state, $A$ (taken as an individual qbit) is not in a superposition state, but in a mixed state. I know that this is a very important basic fact about QM but I still don’t really get it.

  • why is it not possible for $A$ to be both in an entangled state, AND in a superposition “with itself” (i.e. a pure state, rather than a mixed state). I.e. by what principle of quantum mechanics do we know this, and from what does this principle follow?

  • Is there an intuition behind this? I.e. how would quantum mechanics no longer make sense if it weren’t the case.

Not sure if I should ask this on CS or physics SE, but here goes.

I’m reading on quantum computing, and one thing that keeps confusing me is the following basic fact about QM:

Say we have a qbit A, and a qbit B, then two possible quantum states for $A$ are:

$$|+\rangle=\frac {|0\rangle + |1\rangle}{\sqrt 2}$$

$$\frac {|00\rangle + |11\rangle}{\sqrt 2}$$

In the first case, the qbit $A$ is in a quantum superposition between $0$ and $1$. In the second case, the qbits $A$ and $B$ are ALSO in a quantum superposition, but they are now entangled. I understand that there is a difference between these states, in the sense that the second is an entangled state, whereas the first one is not.

However, what I don’t understand, is why, solely from the perspective of $A$, there is a difference between these states. I read that in the second, entangled state, $A$ (taken as an individual qbit) is not in a superposition state, but in a mixed state. I know that this is a very important basic fact about QM but I still don’t really get it.

  • why is it not possible for $A$ to be both in an entangled state, AND in a superposition “with itself” (i.e. a pure state, rather than a mixed state). I.e. by what principle of quantum mechanics do we know this, and from what does this principle follow?

  • Is there an intuition behind this? I.e. how would quantum mechanics no longer make sense if it weren’t the case.

1
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Why can’t a qbit be both entangled and in a pure state?

Not sure if I should ask this on CS or physics SE, but here goes.

I’m reading on quantum computing, and one thing that keeps confusing me is the following basic fact about QM:

Say we have a qbit A, and a qbit B, then two possible quantum states for $A$ are:

$$|+>=\frac {|0> + |1>}{\sqrt 2}$$

$$\frac {|00> + |11>}{\sqrt 2}$$

In the first case, the qbit $A$ is in a quantum superposition between $0$ and $1$. In the second case, the qbits $A$ and $B$ are ALSO in a quantum superposition, but they are now entangled. I understand that there is a difference between these states, in the sense that the second is an entangled state, whereas the first one is not.

However, what I don’t understand, is why, solely from the perspective of $A$, there is a difference between these states. I read that in the second, entangled state, $A$ (taken as an individual qbit) is not in a superposition state, but in a mixed state. I know that this is a very important basic fact about QM but I still don’t really get it.

  • why is it not possible for $A$ to be both in an entangled state, AND in a superposition “with itself” (i.e. a pure state, rather than a mixed state). I.e. by what principle of quantum mechanics do we know this, and from what does this principle follow?

  • Is there an intuition behind this? I.e. how would quantum mechanics no longer make sense if it weren’t the case.