Sabine Hossenfelder, a science YouTuber, talks about asking the following question to ChatGPT 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: I believe chatbots understand part of what they say. Let me explain. March 2023, minute 12:26)

More specifically, the question is whether flipping (without measuring) the spin of one of the particles in 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 'flipping.' What is the operator corresponding to flipping the spin of one of the particles 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?