Sabine Hossenfelder, a science YouTuber, talks about asking the following question to Chat GPT in one of her videos:

If you perform an operation which is not a measurement on one particle in a pair of entangled particles, does that affect the other particle?

(Source: https://youtu.be/cP5zGh2fui0 This question appears around 14:10.)

More specifically, the question is whether switching (without measuring) the spin of one of the EPR pair affects the spin of the other particle.

Sabine says that the answer is "Yes, you can," and ChatGPT failed to generate the correct answer.

What I'd like to know is a mathematical description of this process of 'switching.' What is the operator corresponding to switching the spin of one of the EPR pair without measuring it? How do you show mathematically that such an operator does not affect the other particle if acted on one of the particles?

Any reference to this problem would also be appreciated. Thanks.