Related papers: Identity and difference: how topology helps to und…
The quantum statistics of particles is determined by both the spins and the indistinguishability of quantum states. Here we studied the quantum statistics of partially distinguishable photons by defining the multi-photon…
These lecture notes offer a pedagogical yet concise introduction to topological quantum computing. The material focuses on topological superconductors and Majorana qubits. It concludes with a discussion of more general braiding phenomena.…
Fractional statistics is one of the most intriguing features of topological phases in 2D. In particular, the so-called non-Abelian statistics plays a crucial role towards realizing universal topological quantum computation. Recently, the…
This chapter acknowledges a gap between the ``non-individuals'' interpretation of quantum mechanics and our world of experience, and begins to bridge it. Section 1 states the problem with Abner Shimony's ``Phenomenological principle'';…
In this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics. This model takes into account the different nature of nodes, described by a random…
We investigate quantum tomography in scenarios where prior information restricts the state space to a smooth manifold of lower dimensionality. By considering stability we provide a general framework that relates the topology of the manifold…
We relate topological properties of non-Hermitian systems and observables of quantum open systems by using the Keldysh path-integral method. We express Keldysh Green's functions in terms of effective non-Hermitian Hamiltonians that contain…
We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium -- it is robust against disorder…
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the…
Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover…
This paper discusses relationships between topological entanglement and quantum entanglement. Specifically, we propose that for this comparison it is fundamental to view topological entanglements such as braids as "entanglement operators"…
I review the quantum kinematics of identical particles, which suggests new possibilities, beyond bosons and fermions, in 2+1 dimensions; and how simple flux-charge constructions embody the new possibilities, leading to both abelian and…
In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston's geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement…
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play…
Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of…
Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued…
Quantum gravity may modify the fundamental symmetries that govern identical particles. In particular, noncommutative spacetime frameworks predict deformations of Bose and Fermi statistics. Here we develop a relativistic quantum field theory…
We overwiev the properties of a quantum gas of particles with the intermediate statistics defined by Haldane. Although this statistics has no direct connection to the symmetry of the multiparticle wave function, the statistical distribution…
In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are…
The integration of artificial intelligence (AI) into fundamental science has opened new possibilities to address long-standing scientific challenges rooted in mathematical limitations. For example, topological invariants are used to…