Related papers: Subsystem Complexity and Holography
For a field theory with a gravitational dual, following Susskind's proposal we define holographic complexity for a subsystem. The holographic complexity is proportional to the volume of a co-dimension one time slice in the bulk geometry…
We analyze different holographic complexity proposals for black holes that include corrections from bulk quantum fields. The specific setup is the quantum BTZ black hole, which encompasses in an exact manner the effects of conformal fields…
Motivated by the holographic prescriptions for computing entanglement entropy and complexity, we study the properties of volumes/areas of bulk surfaces. We obtain a simple formula for the shape dependence of holographic entanglement entropy…
We study the evolution of holographic complexity of pure and mixed states in $1+1$-dimensional conformal field theory following a local quench using both the "complexity equals volume" (CV) and the "complexity equals action" (CA)…
Topological phases of matter are often described using auxiliary systems in one extra dimension. I review the one-dimensional cluster state--the simplest quantum state with Symmetry-Protected Topological (SPT) order--as a toy model of…
Holographic superconductor is an important arena for holography, as it allows concrete calculations to further understand the dictionary between bulk physics and boundary physics. An important quantity of recent interest is the holographic…
We study the holographic complexity conjectures for rotating black holes, uncovering a relationship between the complexity of formation and the thermodynamic volume of the black hole. We suggest that it is the thermodynamic volume and not…
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…
We construct a time-dependent expression of the computational complexity of a quantum system which consists of two conformal complex scalar field theories in d dimensions coupled to constant electric potentials and defined on the boundaries…
We apply the recently developed notion of complexity for field theory to a quantum quench through a critical point in 1+1 dimensions. We begin with a toy model consisting of a quantum harmonic oscillator, and show that complexity exhibits…
We conjecture that the quantum complexity of a holographic state is dual to the action of a certain spacetime region that we call a Wheeler-DeWitt patch. We illustrate and test the conjecture in the context of neutral, charged, and rotating…
Using the ``complexity equals action''(CA) conjecture, for an ordinary charged system, it has been shown that the late-time complexity growth rate is given by a difference between the value of $\Phi_{H}Q+\Omega_H J$ on the inner and outer…
We explore a conformal field theoretic interpretation of the holographic entanglement of purification, which is defined as the minimal area of entanglement wedge cross section. We argue that in AdS3/CFT2, the holographic entanglement of…
Our earlier paper "Complexity Equals Action" conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the "Wheeler-DeWitt" patch). We provide calculations for the…
We investigate the impact of measuring one subsystem on the holographic complexity of another. While a naive expectation might suggest a reduction in complexity due to the collapse of the state to a trivial product state during quantum…
We introduce a quasilocal version of holographic complexity adapted to `terminal states' such as spacelike singularities. We use a modification of the action-complexity ansatz, restricted to the past domain of dependence of the terminal…
We study holographic subregion complexity in a spatially anisotropic field theory, which expresses a confinement-deconfinement phase transition. Its holographic dual is a five-dimensional anisotropic holographic model characterized by a Van…
We examine the holographic complexity conjectures in the context of holographic theories of FRW spacetimes. Analyzing first the complexity-action conjecture for a flat FRW universe with one component, we find that the complexity grows as…
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
We observe that the entanglement entropy resulting from tracing over a subregion of an initially pure state can grow faster than the surface area of the subregion (indeed, proportional to the volume), in contrast to examples studied…