Information is that which reduces uncertainty, wholly or in part. Similarly, anti-information is that which increases uncertainty. It is negative information.
Noise on a noisy communication channel is an example of anti-information. According to Shannon's Channel Coding Theorem the entropy of the noise must be subtracted to obtain the channel capacity that remains available for reliable communication.
The gambling industry has made a business out of selling anti-information. People are willing to pay for anti-information. The increase in uncertainty enables them to savor the information that they subsequently receive when the uncertainty is finally resolved.
The term anti-information was introduced by Koos Verhoeff in the 1970s while teaching informatics at the Erasmus University Rotterdam.