Related papers: A note on weight systems which are quantum states
We present the construction of a new state sum model for $4d$ Lorentzian quantum gravity based on the description of quantum simplicial geometry in terms of edge vectors. Quantum states and amplitudes for simplicial geometry are built from…
We present applications of the representation theory of Lie groups to the analysis of structure and local unitary classification of Werner states, sometimes called the {\em decoherence-free} states, which are states of $n$ quantum bits left…
We introduce the concept of quantum weight as a ground state property of quantum many-body systems that is encoded in the static structure factor and characterizes density fluctuation at long wavelengths. The quantum weight carries a wealth…
The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…
We discuss how a large class of incompressible quantum Hall states can be characterized as highest weight states of different representations of the \Winf algebra. Second quantized expressions of the \Winf generators are explicitly derived…
Quantum computation in the one-way model requires the preparation of certain resource states known as cluster states. We describe how the construction of continuous-variable cluster states for optical quantum computing relate to the…
The relationship between the GNS representations associated to states on a quasi *-algebra, which are {\em local modifications} of each other (in a sense which we will discuss) is examined. The role of local modifications on the spatiality…
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
The phase space for a system of $n$ qubits is a discrete grid of $2^{n} \times 2^{n}$ points, whose axes are labeled in terms of the elements of the finite field $\Gal{2^n}$ to endow it with proper geometrical properties. We analyze the…
We present state sums for quantum link invariants arising from the representation theory of $U_q(\mathfrak{gl}_{N|M})$. We investigate the case of the $N$-th exterior power of the standard representation of $U_q(\mathfrak{gl}_{N|1})$ and…
We develop a model of one-dimensional (Conformal) Quantum Gravity. By discussing the connection between Goldstone and Gauge theories, we establish that this model effectively computes the partition function of the Schwarzian theory where…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
In this work, based on a recently introduced localization scheme for scalar fields, we argue that the geometry of the space-time, where the particle states of a scalar field are localized, is intimately related to the quantum entanglement…
In this paper the generalized quantum states, i.e. positive and normalized linear functionals on $C^{*}$-algebras, are studied. Firstly, we study normal states, i.e. states which are represented by density operators, and singular states,…
The concept of quantum representation of finite groups (QRFG) has been a fundamental aspect of quantum computing for quite some time, playing a role in every corner, from elementary quantum logic gates to the famous Shor's and Grover's…
Non-manifest symmetries are an important feature of quantum field theories (QFTs), and yet their characteristics are not fully understood. In particular, the construction of the charge operators associated with these symmetries is…
We introduce a quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning. The quantum circuit consists of a sequence of parameter dependent unitary transformations which acts…
The n-qubit real equally weighted states are employed in some quantum algorithms including Deutsch-Jozsa, Grover, Simon, and so on. We qualitatively investigate the entanglement properties of n-qubit real equally weighted states. Firstly,…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
Different constructions for Hilbert state space for constrained systems are investigated. Properties of Gaussian states analogous to quantum mechanical Gaussian wave functions are studied. Their evolution for quadratic Hamiltonian case are…