  If simple entropy in the Bekenstein-Hawking area law for a Schwarzschild
black hole is replaced with 'negative' quantum conditional entropy, which
quantifies quantum entanglement, of positive-energy particles of the black hole
relative to its outside, a paradox with the original pair-creation picture of
Hawking radiation, the first law for black hole mechanics and quantum mechanics
is resolved. However, there was no way to judge experimentally which area law
is indeed adopted by black holes. Here, with the no-hair conjecture, we derive
the perfect picture of a second law of black hole thermodynamics for any black
hole from the modified area law, rather than Bekenstein's generalized one from
the original area law. The second law is testable with an event horizon
telescope, in contrast to Bekenstein's. If this is confirmed, the modified area
law could be exalted to the first example of fundamental equations in physics
which cannot be described without the concept of quantum information.
