Related papers: Quantum Rotatability
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators in the space of functions on a Hilbert space which are square integrable with respect to…
It is demonstrated that, making minimal changes in ordinary quantum mechanics, a reasonable irreversible quantum mechanics can be obtained. This theory has a more general spectral decompositions, with eigenvectors corresponding to unstable…
Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At…
We study the structure of the inverse limit of the graded algebras of local unitary invariant polynomials using its Hilbert series. For k subsystems, we conjecture that the inverse limit is a free algebra and the number of algebraically…
Quantum gravity may modify the fundamental symmetries that govern identical particles. In particular, noncommutative spacetime frameworks predict deformations of Bose and Fermi statistics. Here we develop a relativistic quantum field theory…
The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum…
We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family $\GR \to B$ of Lie groups (these families are called ``gauge-invariant families'' in what follows). If the fibers…
Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well.…
Within the framework of the individuality interpretation of quantum theory (QT), the basic equations of QT cannot be derived from the basic equations of classical mechanics (CM). The unbridgeable gap between CM and QT is given by the fact…
We determine the quantum variance of a sequence of families of automorphic forms on a compact quotient arising from a non-split quaternion algebra. Our results compare to those obtained by Luo--Sarnak, Zhao, and Sarnak--Zhao on the modular…
Researchers have long been aiming to understand how the characteristics of Quantum Theory and General Relativity combine to account for regimes in their interface. One reason why this is a hard task is how differently the theories approach…
In continuous-variable quantum computation, identifying key elements that enable a quantum computational advantage is a long-standing issue. Starting from the standard results on the necessity of Wigner negativity, we develop a…
We link the notion causality with the orientation of the 2-complex on which spin foam models are based. We show that all current spin foam models are orientation-independent, pointing out the mathematical structure behind this independence.…
Given a semisimple stable autonomous tensor category over a field $K$, to any group presentation with finite number of generators we associate an element $Q(P)\in K$ invariant under the Andrews-Curtis moves. We show that in fact, this is…
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -- a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M…
We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by…
Parametric fluctuations or stochastic signals are introduced into the control pulse sequence to investigate the feasibility of random control over quantum open systems. In a large parameter error region, the out-of-order control pulses work…
In this article we review the standard versions of the Central and of the Levy-Gnedenko Limit Theorems, and illustrate their application to the convolution of independent random variables associated with the distribution known as…
We present a relativistic formulation of noncommutative mechanics were the object of noncommutativity $\theta^{\mu\nu}$ is considered as an independent quantity. Its canonical conjugate momentum is also introduced, what permits to obtain an…
One of the most prominent features of quantum entanglement is its invariability under local unitary transformations, which implies the degree of entanglement remains constant during free-space propagation. While this is true for quantum and…