Related papers: Holographic State Complexity from Group Cohomology
We study ensembles described by density matrices with potentially nontrivial topological features. In particular, we study a class of symmetry protected topological (SPT) phases under various types of decoherence, which can drive a pure SPT…
In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the…
In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new models and new topological phases which…
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
We describe an explicit mechanism for the emergence of a dynamical holographic bulk from the structure of entanglement in a quantum state. We start with a generic system in complete isolation, assuming it has a classical limit involving…
With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
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…
We study the complexity of Gaussian mixed states in a free scalar field theory using the 'purification complexity'. The latter is defined as the lowest value of the circuit complexity, optimized over all possible purifications of a given…
I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…
In this paper, we holographically quantify the entanglement and complexity for mixed states by following the prescription of purification. The bulk theory we consider in this work is a hyperscaling violating solution, characterized by two…
Symmetry-protected topological phases (SPT) are short-range entangled gapped states protected by global symmetry. Nontrivial SPT phases cannot be adiabatically connected to the trivial disordered state(or atomic insulator) as long as…
We perform a comparative study of the time dependence of the holographic quantum complexity of some space like singular bulk gravitational backgrounds. This is done by considering the two available notions of complexity, one that relates it…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
Two quantum theories which look different but are secretly describing the same low-energy physics are said to be dual to each other. When realized in the Topological Holography formalism, duality corresponds to changing the gapped boundary…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
We investigate the physics of one-dimensional symmetry protected topological (SPT) phases protected by symmetries whose symmetry generators exhibit spatial modulation. We focus in particular on phases protected by symmetries with linear…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
Two global symmetries are holo-equivalent if their algebras of local symmetric operators are isomorphic. Holo-equivalent classes of global symmetries are classified by gappable-boundary topological orders (TO) in one higher dimension…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…