Is it possible to compare two systems in superposition?

Is it possible to compare if two systems in a superposition are equal or not equal to each other, i.e. two systems with two electrons in superposition?

At first:

1. Superposition of two electrons (state unknown)

2. Superposition of two electrons (we know that after the measurement the value will be $$01$$)

We compare the two superpositions:

Comparison of 1 and 2 would return false, so we know that 1. after the measurement is not $$01$$, but another value, i.e. $$10$$

Does the no-cloning theorem apply in a manner that I could not create a clone of the first system and then compare it with 1 to get "true"?

Edit: It could very well be that I misunderstood something, I'm only an amateur in physics.

• Do you want to check without disturbing the states? Also, do you know the possible states? Mar 29, 2019 at 13:40
• Yes, without disturbing the states & either way for the possible states Mar 29, 2019 at 13:50
• Can you clarify what you are asking? Do you mean that system 1, after measurement is in a superposition of states 0 and 1? And what do you mean by 'comparison' would return false?
– gabe
Mar 29, 2019 at 13:51
• Do you know what are the possible superposition states? Or are they arbitrary? Mar 29, 2019 at 13:52
• In quantum theory, we usually say that 2 electrons are identical. Therefore the state is neither 1. or 2. but an anti-symmetric combination $\frac{1}{\sqrt{2}}(|1>|0>-|0>|1>)$. This postulate directly gives the Pauli principle for fermions. en.wikipedia.org/wiki/… Mar 29, 2019 at 13:54