# Effect of quantum entanglement on measurement

I'm taking a quantum information systems class and thought of this while trying to wrap my head around some material, so I apologize if this comes off as dumb or founded on misunderstandings.

Say you have a system consisting of three qubits a, b, and c, where qubits b and c are entangled in a Bell state, but you're not aware of this fact. You take a measurement of qubits a and b, inherently losing the information/collapsing the wavefunction (?).

As qubit c was in an entangled state with qubit b, but was never directly or knowingly measured, does the measurement also affect the third qubit, causing it to lose its information as well? I feel like the answer is yes but it's interesting to think about.

TLDR: If a qubit is measured in a forest, but no one is around to take the measurement it, does it still affect its state?

• You might be interested in this work: nature.com/articles/s41567-020-0990-x Sep 9, 2020 at 10:19
• @brzepkowski thanks that does look interesting, I'll check it out Sep 10, 2020 at 1:20

It depends on what exactly you mean by "affected".

First of all, I'd say from your description that your "a" does not actually enter the discussion. The question is then essentially: suppose Alice (A) and Bob (B) have entangled states, and A performs a measurement; does this affect B's state?

The knowledge acquired by A with her measurement allows her to predict something about B's (eventual) measurement results. Assuming for example they share a maximally entangled state, then A knows that if B uses her same measurement basis, then he'll find her same outcome, i.e. their measurement results will be correlated.

Does this mean that A's act of measuring affected Bob's state? Not really, because if they don't exchange information about their respective measurement outcomes, there is no way for Bob to know anything about what Alice did to her state, and vice versa. It's hard to maintain that Alice affected Bob's state in any way, if from Bob's perspective there is no observable modification on the state caused by Alice's actions.

The situation is more akin to the states being correlated, albeit this type of correlation is stronger than what is possible classically.

There's also plenty of posts on similar topics on physics.SE. E.g. If two particles are entangled and you collapse the wave function of one of the particles. Does the other particle collapse as well?.

• Thanks for your response! You're right in that the third qubit I included wasn't really necessary to the question. I think I was confusing knowing the amplitudes of an entangled qubit with actually performing a measurement operation on it. Sep 10, 2020 at 1:24