Holographic Interpretation of Relative State Complexity
arXiv:2004.07960 · doi:10.3390/universe6080100
Abstract
We investigate a large- CFT in a high-energy pure state coupled to a small auxiliary system of weakly-interacting degrees of freedom, and argue the relative state complexity of the auxiliary system is holographically dual to an effective low-energy notion of computational cost in the bulk, \textit{i.e.} to the minimal depth of the quantum circuit required to decode its gravitational dual. In light of this, using Nielsen's approach, a new measure of quantum chaos in terms of the evolution of circuit complexity is proposed. It suggests that studying the evolution of circuit complexity of the auxiliary system can teach us about the chaotic properties of the large- CFT. This new diagnostic for quantum chaos has important implications for the interior dynamics of evaporating black holes as it implies the radiated Hawking cloud is pseudorandom.
arXiv comment18 pages, 2 figures. Discussions expanded, changes to the outline
References in corpus (29)
- A bound on chaos
- Comments on the Sachdev-Ye-Kitaev model
- Towards a derivation of holographic entanglement entropy
- Cool horizons for entangled black holes
- Ultimate physical limits to computation
- Complexity Equals Action
- Complexity and Shock Wave Geometries
- Time Evolution of Entanglement Entropy from Black Hole Interiors
- The Spectrum in the Sachdev-Ye-Kitaev Model
- Complexity, action, and black holes
- Environment-independent decoherence rate in classically chaotic systems
- Aspects of generic entanglement
- Random Quantum Circuits are Approximate 2-designs
- The Second Law of Quantum Complexity
- Quantum Computation vs. Firewalls
- Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
- Optimal control, geometry, and quantum computing
- Black holes, complexity and quantum chaos
- How big is a black hole?
- Chaos and Complexity in Quantum Mechanics
- Quantum Complexity of Time Evolution with Chaotic Hamiltonians
- The Complexity Geometry of a Single Qubit
- Convergence Conditions for Random Quantum Circuits
- The ghost in the radiation: Robust encodings of the black hole interior
- Holographic Complexity and Volume
- Time evolution of the complexity in chaotic systems: concrete examples
- Butterflies from Information Metric
- Stringy Effects and the Role of the Singularity in Holographic Complexity
- Quantum Complexity and Chaos in Young Black Holes