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Isaac Newton Institute for Mathematical Sciences

Quantum Gravity and Quantum Information

Locked information and the black hole information loss problem

Author: John Smolin (IBM)


Recently, a new and purely quantum effect has been discovered in which a small amount of information acts as a key that can unlock a much larger amount of information. Classically, the accessible mutual information about a random variable is never less than the total amount of entropy in the random variable minus the size of the key. Quantum-mechanically, the accessible information without the key can vanishing compared to the total entropy available when the key is known.

This effect may help resolve the black hole infomration loss problem: If the information leaks out of an evaporating black hole while appearing random until the hole is of Plank size, then the plank scale black hole must someone "encrypt" all the information that has radiated away so far while itself having very small entropy. This was thought to be impossible but is precisely the case in the locking effect.