The security of adding random noise many time pad In may application, I have a series of real number $\{v_1, v_2, \ldots, v_N\}, v_i\in\mathbb{R}$. To protect them, I add a random noise $r\in\mathbb{R}$ to each themselves like one-time-pad encryption scheme. But due to some more requirements of optimization we only want to generate and use a random noise $r$ instead of generating one time pad. Is this model is secure and which level of security can I obtain?
Too tricky for a comment...

Conceptually, your scheme is 110% information theoretic secure, as it's a one time pad($ \downarrow $). But since we tend to use octet based computer architecture these days, $  \mathbb{Z}  $ is more appropriate.

Note 1. Ensure $ |r| \ge |v| $.

Note 2. Don't want to patronise, but the one time pad is thee most contentious and misunderstood aspect of cryptography ever invented. Especially on this forum. Is $r$ truly random or just pseudo-random? It's worrisome that I read 'generate' in a kinda algebraic context...