Abstract
This essay argues that the AdS/CFT correspondence, as a limits-based model of undecidability and non-computability, highlights quantum reality as being not only information-theoretic, but rigorously computational as a mathematically-sound domain with built-in cryptographic security features such that black holes provide their own zero-knowledge proofs. The AdS/CFT correspondence (anti-de Sitter space/conformal field theory) is a hypothesis asserting that any physical system with a bulk volume (such as a black hole) can be described by a boundary theory in one fewer dimensions. The result is that a seemingly complex incomputable system in a chaotic bulk volume is rendered solvable as a boundary theory in one fewer dimensions. Nature’s quantum security features provide an even more robust computational domain than was appreciated. These include the no-cloning theorem, the no-measurement principle, error correctability, provably-random statistical signatures per the SEI properties of quantum objects (superposition, entanglement, and interference), and zero-knowledge proofs (proofs revealing no information except whether a proposition is True or False). The zero-knowledge property is implicated in quantum computational systems in that a traditional prover-verifier relationship (an external prover) is not necessary because the quantum computer performs its own truth verification as part of the proof. The implication is that quantum computing has zero-knowledge proof technology built into it as a feature. BQP (the class of problems solvable with a quantum computer) computes quickly and soundly enough to provide its own computationally-verifiable proof. The consequence is that any quantum computational domain, including black holes, performs its own truth verification through zero-knowledge proofs. The result of this work is that the AdS/CFT correspondence is demonstrated as a juggernaut formulation that ties together not only physics and information theory in a limits-based computational method as a feature for analyzing problems in contemporary physics, but also incorporates a new level of soundness with cryptographic mathematical properties.
Melanie Swan