Holographic fluctuations and the principle of minimal complexity

Wissam A Chemissany, Tobias J. Osborne

We discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. We review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state. We describe how this idea may be extended to determine the relationship between the fluctuations of the bulk holographic geometry and the fluctuations of the boundary low-energy subspace. In this way we obtain, for every quantum system, an Einstein-like equation of motion for what might be interpreted as a bulk gravity theory dual to the boundary system.

Javier Martín García

Koji Hashimoto, Norihiro Iizuka, Sotaro Sugishita

In this paper, we argue that holographic complexity should be a basis-dependent quantity. Computational complexity of a state is defined as a minimum number of gates required to obtain that state from the reference state. Due to this minimality, it satisfies the triangle inequality and can be regarded as a (discrete version of) distance in the Hilbert space. However, we show a no-go theorem that any basis-independent distance cannot reproduce the behavior of the holographic complexity. Therefore, if holographic complexity is dual to a distance in the Hilbert space, it should be basis dependent; i.e., it is not invariant under a change of the basis of the Hilbert space.

David D. Blanco, Horacio Casini, Ling-Yan Hung +1 more

Koustubh Kabe

Paweł Caputa, Masamichi Miyaji, Tadashi Takayanagi +1 more

We explore a conformal field theoretic interpretation of the holographic entanglement of purification, which is defined as the minimal area of the entanglement wedge cross section. We argue that, in AdS_{3}/CFT_{2}, the holographic entanglement of purification agrees with the entanglement entropy for a purified state, obtained from a special Weyl transformation, called path-integral optimizations. By definition, this special purified state has minimal path-integral complexity. We confirm this claim in several examples.