相关论文: Quantum Geometry and Wild embeddings as quantum st…

In this paper we try to define the higher dimensional analogues of vertex algebras. In other words we define algebras which we hope have the same relation to higher dimensional quantum field theories that vertex algebras have to one…

We study the behaviors of quantum groups under an edge contraction. We show that there exists an explicit embedding induced by an edge contraction operation. We further conjecture that this explicit embedding is a section of an explicit…

The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…

The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…

In open quantum systems, entanglement can vanish faster than coherence. This phenomenon is usually called sudden death of entanglement. In this paper sudden death of entanglement is discussed from a geometrical point of view, in the context…

A random field that is empirically equivalent to the quantized electromagnetic field is constructed. A mapping between the creation and annihilation operator algebras of a random field and of the quantized electromagnetic field provides a…

The wild de Rham spaces parameterize isomorphism classes of (stable) meromorphic connections, defined on principal bundles over wild Riemann surfaces. Working on the Riemann sphere, we will deformation-quantize the standard open part of de…

Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover,…

The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the…

We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum and entanglement entropy (EE) of the density matrix for…

The state vector evolution in the interaction of measured pure state with the collective quantum system or the field is analyzed in a nonperturbative QED formalism. As the model example the measurement of the electron final state scattered…

Recently, a connection has been shown between certain geometric quantities and quantum information theory. In this paper, we demonstrate that geometric quantities such as area and volume can emerge directly from entangled multi-qubit…

We present a geometrical description of the space of density states of a quantum system of finite dimension. After presenting a brief summary of the geometrical formulation of Quantum Mechanics, we proceed to describe the space of density…

I start with a scenario where the universe is an abstract space $\mathcal{M}$ having $d$ dimensions. There is a two dimensional surface embedded in it. Embedding is a map from the embedded surface to $\mathcal{M}$ that has a field theory…

This overview paper reviews several results relating the representation theory of quivers to algebraic geometry and quantum group theory. (Potential) applications to the study of the representation theory of wild quivers are discussed. To…

It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on…

Recently, a geometric embedding of the classical space and classical phase space of an n-particle system into the space of states of the system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the…

We introduce a sum-of-squares SDP hierarchy approximating the ground-state energy from below for quantum many-body problems, with a natural quantum embedding interpretation. We establish the connections between our approach and other…

The notion of entanglement can be naturally extended from quantum-states to the level of general quantum evolutions. This is achieved by considering multi-partite unitary transformations as elements of a multi-partite Hilbert space and then…

Consider a bipartite entangled system half of which falls through the event horizon of an evaporating black hole, while the other half remains coherently accessible to experiments in the exterior region. Beyond complete evaporation, the…