Related papers: Complexity and Shock Wave Geometries
The internal disorder of the two-dimensional confined hydrogenic atom is numerically studied in terms of the confinement radius for the 1\textit{s}, 2\textit{s}, 2\textit{p} and 3\textit{d} quantum states by means of the statistical…
The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation…
The Einstein- Gauss- Bonnet (EGB) gravity is an important modification of the Einstein theory of gravity and, for many gravitational phenomena, the Gauss- Bonnet (GB) correction term leads to drastic differences. In this paper, we study…
An important conjecture within the AdS/CFT correspondence relates holographic spacetime to the quantum computational complexity of the dual quantum field theory. However, the quantitative understanding of this relation is still an open…
We present a general construction of a geometric notion of circuit complexity for Gaussian states (both bosonic and fermionic) in terms of Riemannian geometry. We lay out general conditions that a Riemannian metric function on the space of…
The quantum gravity has great difficulties with application of the probability notion. In given article this problem is analyzed according to algorithmic viewpoint. According to A.N. Kolmogorov, the probability notion can be connected with…
We revisit the entanglement of a Schwinger pair created by external fields of arbitrary strength, using a holographic dual description of QCD. When external fields are strong in comparison to the string tension, the entanglement is…
How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic convex…
It is shown that experiments of the Einstein-Podolski-Rosen type are the natural consequence of the groupoid approach to noncommutative unification of general relativity and quantum mechanics. The geometry of this model is determined by the…
We give arguments for the existence of a thermodynamics of quantum complexity that includes a "Second Law of Complexity". To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of $K$…
In this article, we investigate various physical implications of quantum circuit complexity using squeezed state formalism of Primordial Gravitational Waves (PGW). Recently quantum information theoretic concepts, such as entanglement…
The ER=EPR conjecture states that quantum entanglement between boundary degrees of freedom leads to the emergence of bulk spacetime itself. Although this has been tested extensively in String Theory for asymptotically anti-de Sitter…
We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a…
We study the time-evolution of the two dimensional multi-component Bose-Einstein condensate in an external harmonic trap with arbitrary time-dependent frequency. We show analytically that the time-evolution of the total mean-square radius…
How complex is the structure of quantum geometry? In several approaches, the spacetime atoms are obtained by the SU(2) intertwiner called quantum tetrahedron. The complexity of this construction has a concrete consequence in recent efforts…
In statistical mechanics entropy is a measure of disorder obeying Boltzmann's formula $S=\log{\cal N}$, where ${\cal N}$ is the accessible phase space volume. In black hole thermodynamics one associates to a black hole an entropy…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
A geometric theory of brane-worlds with large or non-compact extra dimensions is presented. It is shown that coordinate gauge independent perturbations of the brane-world correspond to the Einstein-Hilbert dynamics derived from the…
We propose a fundamental duality between the geometric properties of spacetime and the informational content of quantum fields. Specifically, we establish that the curvature of spacetime is directly related to the entanglement entropy of…
We introduce "binding complexity", a new notion of circuit complexity which quantifies the difficulty of distributing entanglement among multiple parties, each consisting of many local degrees of freedom. We define binding complexity of a…