Related papers: Group Theory and Representation Theory for Identic…
Typical elements of quantum networks are made by identical systems, which are the basic particles constituting a resource for quantum information processing. Whether the indistinguishability due to particle identity is an exploitable…
We present a conceptually clear introduction to quantum theory, deriving the theory from scratch from the point of view of quantum information. Different subsets of these lectures were taught to a wide variety of audiences, including…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
Despite its name, Quantum Field Theory (QFT) has been built to describe interactions between localizable particles. For this reason the actual formalism of QFT is partly based on a suitable generalization of the one already used for systems…
We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…
We consider entanglement in a system of fixed number of identical particles. Since any operation should be symmetrized over all the identical particles and there is the precondition that the spatial wave functions overlap, the meaning of…
The existence of fundamentally identical particles represents a foundational distinction between classical and quantum mechanics. Due to their exchange symmetry, identical particles can appear to be entangled -- another uniquely quantum…
Induced representations for quantum groups are defined starting from coisotropic quantum subgroups and their main properties are proved. When the coisotropic quantum subgroup has a suitably defined section such representations can be…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application…
According to the Received View identical quantum particles are a previously unknown kind of objects that do not possess individuality. In this Chapter we discuss this view, criticize it, and propose an alternative. According to this…
Quantum information science is an exciting, wide, rapidly progressing, cross-disciplinary field, and that very nature makes it both attractive and hard to enter. In this primer, we first provide answers to the three essential questions that…
Entanglement is nowadays considered as a key quantity for the understanding of correlations, transport properties, and phase transitions in composite quantum systems, and thus receives interest beyond the engineered applications in the…
This thesis investigates quantum cloning and related quantum entanglement problems using core concepts of representation theory, in particular those associated with the symmetric group. The research explores Schur-Weyl duality and its…
The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced,…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…