相关论文: Quantum Knots

Quantum networks illustrate the use of connected nodes of quantum systems as the backbone of distributed quantum information processing. When the network nodes are entangled in graph states, such a quantum platform is indispensable to…

For classical knots, there is a concept of (semi)meander diagrams; in this short note we generalize this concept to virtual knots and prove that the classes of meander and semimeander diagrams are universal (this was known for classical…

Relative self-linking and linking "numbers" for pairs of knots in oriented 3-manifolds are defined in terms of intersection invariants of immersed surfaces in 4-manifolds. The resulting concordance invariants generalize the usual…

This paper introduces the concept of a Fourier knot. A Fourier knot is a knot that is represented by a parametrized curve in three dimensional space such that the coordinate functions are finite Fourier series in the parameter. The…

This paper studies knots in three dimensional projective space. Our technique is to associate a virtual link to a link in projective space so that equivalent projective links go to equivalent virtual links (modulo a special flype move). We…

We introduce a new concept of Quantum Wrapper Networking, which enables control, management, and operation of quantum networks that can co-exist with classical networks while keeping the requirements for quantum networks intact. The quantum…

A Quantum Internet, i.e., a global interconnection of quantum devices, is the long term goal of quantum communications, and has so far been based on two-dimensional systems (qubits). Recent years have seen a significant development of…

The classical knot recognition problem is the problem of determining whether the virtual knot represented by a given diagram is classical. We prove that this problem is in NP, and we give an exponential time algorithm for the problem.

A quantum network consists of independent sources distributing entangled states to distant nodes which can then perform entangled measurements, thus establishing correlations across the entire network. But how strong can these correlations…

Lord Kelvin's pioneering hypothesis that the identity of atoms is knots of vortices of the aether had a profound impact on the fields of mathematics and physics despite being subsequently refuted by experiments. While knot-like excitations…

Quantum mechanics allows coherent superposition between different states of matter. This quality is responsible for major non-classical phenomena that occur in quantum systems. Beyond states, coherent superpositions are also possible…

Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…

The knots-quivers correspondence states that various characteristics of a knot are encoded in the corresponding quiver and the moduli space of its representations. However, this correspondence is not a bijection: more than one quiver may be…

Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this,…

We give a pedagogical introduction to quantum discord. We the discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy…

A knot is an an embedding of a circle into three-dimensional space. We say that a knot is unknotted if there is an ambient isotopy of the embedding to a standard circle. By representing knots via planar diagrams, we discuss the problem of…

Understanding the relationship between various different forms of nonclassicality and their resource character is of great importance in quantum foundation and quantum information. Here, we discuss a quantitative link between quantum…

In the classical world one can construct two identical systems which have identical behavior and give identical measurement results. We show this to be impossible in the quantum domain. We prove that after the same quantum measurement two…

Exact solution to many problems in mathematical physics and quantum field theory often can be expressed in terms of an algebraic curve equipped with a meromorphic differential. Typically, the geometry of the curve can be seen most clearly…

Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…