Yes they canOnce again, NO, he can't.
The Atomic Energy Act of 1954 sets requirements for protection of information about nuclear weapons and special nuclear materials. Such information is "classified from birth", unlike all other sensitive information, which must be classified by some authorized individual. However, authorized classifiers still must determine whether documents or material are classified or restricted.
"Born secret" and "born classified" are both terms which refer to a policy of information being classified from the moment of its inception, usually regardless of where it was created, and usually in reference to specific laws in the United States that are related to information that describes the operation of nuclear weapons.
Do presidents have 'the ability to declassify anything'?
The blockbuster article in The Washington Post saying President Donald Trump had "revealed highly classified information
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