# Entanglement invariant under local basis change?

Today in the lecture the professor said that if we have an entangled state between two systems A and B

$$\mid \psi_{AB} \rangle = \frac{1}{\sqrt2}(\mid 00\rangle+\mid 11\rangle)$$

There is no local unitary we could apply to change this entanglement. In other words for example

$$U_A \otimes \mathbb{I}_B\mid\psi_{AB}\rangle$$

$$\mid\psi_{AB}\rangle$$ will remain entangled no matter what unitary we use here.

I wanted to find out more about this behavior. Can anyone link me sources, tell me maybe more about this or even tell me whether this property also holds for classically correlated systems or this is a unique feature of entanglement?

• Didn't you just ask almost the same question and then delete it? You should edit your questions. – Norbert Schuch Jan 18 '19 at 21:09
• "whether this property also holds for classically correlated systems" -- which property? – Norbert Schuch Jan 18 '19 at 21:10
• @Norbert Schuch I did but found, that it does not explain what I mean well enough. As you see it can be explained in a much more compact way. The 'property' of locally invariant quantum correlations. But as stated in the question I'd be already super happy if one could show me papers discussing the behavior I showcased in the question. That local unitaries can't change entanglement. – CatoMaths Jan 18 '19 at 21:34
• You should read about Schmidt decomposition. Is is in any quantum info textbook. (P.S.: Deleting questions is bad for your internal score, they say. Editing is better.) – Norbert Schuch Jan 18 '19 at 21:39