Related papers: Quantum Dilogarithm
The similarity transformations of quantum orthogonal groups are developed and FRT theory is reformulated to the Cartesian basis. The quantum orthogonal Cayley-Klein groups are introduced as the algebra functions over an associative algebra…
We suggest a new strategy for proving large $N$ duality by interpreting Gromov-Witten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau threefold as different characterizations of the same holomorphic function. For the resolved…
Quantum entanglement was first recognized as a feature of quantum mechanics in the famous paper of Einstein, Podolsky and Rosen [18]. Recently it has been realized that quantum entanglement is a key ingredient in quantum computation,…
Starting with the first-order singular Lagrangian, the problem of the quantization of a dynamical system constrained to a submanifold embedded in the higher-dimensional Euclidean space is investigated within the framework of operatorial…
The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
We exhibit and discuss "wild" analogues of the five-term quantum dilogarithm identity. We derive these from the representation theory of quivers, using motivic wall-crossing, the geometricity of motivic Donaldson-Thomas invariants, and…
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We show that if no entanglement is envolved then…
We construct the (enhanced Rogers) dilogarithm function from the spin Chern-Simons invariant of C*-connections. This leads to geometric proofs of basic dilogarithm identities and a geometric context for other properties, such as the…
When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become…
It is shown that certain natural quantum logic gates, {\it i.e.} unitary time evolution matrices for spin-\frac{1}{2} quantum spins, can be represented as sums, with appropriate phases, over classical logic gates, in a direct analogy with…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
Using the newly introduced general ordering theorem (GOT) by Sh\"ahandeh and Bazrafkan, we derive and generalize some quantum optical identities and give their applications.
Holant problems are intimately connected with quantum theory as tensor networks. We first use techniques from Holant theory to derive new and improved results for quantum entanglement theory. We discover two particular entangled states…
We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…
For any homogeneous identity between $q$-minors, we provide an identity between $P,Q$-minors.
In this paper, we consider three types of polynomial equations in quantum computer: linear divisibility equation, which belongs to a special type of binary-quadratic Diophantine equation; quadratic congruence equation with restriction in…
For a wide set of quantum systems it is demonstrated that the quantum regime can be considered as the transient phase while the final classical statistical regime is a permanent state. A basis where exact matrix decoherence appears for…