Related papers: Feynman's Integral is About Mutually Unbiased Base…
An efficient method for assessing the quality of quantum state tomography is developed. Special attention is paid to the tomography of multipartite systems in terms of unbiased measurements. Although the overall reconstruction errors of…
We provide evidence that quantum mechanics can be interpreted as a rational algorithm for finding the least complex description for the correlations in the outputs of sensors in a large array. In particular, by comparing the…
The Feynman path integral is defined over the space $\mathbb{R}^T$ of all possible paths; it has been a powerful tool to develop Quantum Mechanics. The absolute value of Feynman's integrand is not integrable, then Lebesgue integration…
The Feynman path integral for nonrelativistic quantum electrodynamics is studied mathematically of a standard model in physics, where the electromagnetic potential is assumed to be periodic with respect to a large box and quantized thorough…
The question of quantifying the sharpness (or unsharpness) of a quantum mechanical effect is investigated. Apart from sharpness, another property, bias, is found to be relevant for the joint measurability or coexistence of two effects.…
The new emerging quantum physics - quantum computing conceptual bridge, mandates a ``grand unification'' of space-time-matter and quantum information (all quantized), with deep implications for science in general. The major physics…
Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases…
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…
In this paper we show that interaction-free measurements, which have been object of much discussion in the last few decades, can be explained in a natural and intuitive way in the framework of complex nonlinear quantum physics, contrary to…
Integration By Parts (IBP) is an important method for computing Feynman integrals. This work describes a formulation of the theory involving a set of differential equations in parameter space, and especially the definition and study of an…
We consider the quantum computational process as viewed by an insider observer: this is equivalent to an isomorphism between the quantum computer and a quantum space, namely the fuzzy sphere. The result is the formulation of a reversible…
In this talk we discuss mathematical structures associated to Feynman graphs. Feynman graphs are the backbone of calculations in perturbative quantum field theory. The mathematical structures -- apart from being of interest in their own…
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…
Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum…
Quantum coherence is a key resource in quantum information processing scenarios, and quantifying coherence is an important task for both quantum foundation and quantum technology. However, until now, all most of coherence measures are…
We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.
A Feynman formula is a representation of a solution of an initial (or initial-boundary) value problem for an evolution equation (or, equivalently, a representation of the semigroup resolving the problem) by a limit of $n$-fold iterated…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
We investigate $\varepsilon$-factorised differential equations, uniform transcendental weight and purity for Feynman integrals. We are in particular interested in Feynman integrals beyond the ones which evaluate to multiple polylogarithms.…
Pivotal within quantum physics, the concept of quantum incompatibility is generally related to algebraic aspects of the formalism, such as commutation relations and unbiasedness of bases. Recently, the concept was identified as a resource…