[abarker]

In quantum information theory the ability of Alice to instantaneously change Bob's quantum state (and hence measurement probabilities) is referred to as quantum steering. No information can be sent, but the influencing effect can be defined and observed. Steering is distinct from both Bell-nonlocality and nonseparability. See, e.g., [1] and later papers.

[1] https://arxiv.org/abs/quant-ph/0612147

[da-x]

Do you mean that it was proven that observation affects the other end immediately, or is it only just a theory? If so, how it was proven, without it also being useful for sending information?

[abarker]

It is a theory in the sense that it is epistemic. Bob's quantum state changes depending on Alice's measurement, essentially collapsing the probability distribution to the conditional probability distribution. As science it cannot be proven, but the empirical results match the model. The paper I cited defines precise protocols to define terms like "steerable states." This is standard quantum theory, so the no-communication theorem still applies.

Is the quantum state also ontic, and in what sense? Those are open questions of interpretation.