Related papers: Uncertainty relations and joint numerical ranges
Continuous symmetries generated with observables of a quantum theory in the Minkowski spacetime are discussed. An example of an originated in this way algebra of observables is the algebra of observables of the canonical quantum theory,…
Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance…
A theory of joint nonideal measurement of incompatible observables is used in order to assess the relative merits of quantum tomography and certain measurements of generalized observables, with respect to completeness of the obtained…
Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…
A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical…
One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
Establishing a notion of the quantum state that applies consistently across space and time could be a crucial step toward formulating a relativistic quantum theory. We give an operational meaning to multipartite quantum states over…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…
In this article, we provide theoretical support for the use of geometric measures of nonclassicality as a general tool to identify quantum phase transitions. We argue that divergences in the susceptibility of any geometric measure of…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
The measurement range problem, where one cannot determine the data outside the range of the detector, limits the characterization of entanglement in high-dimensional quantum systems when employing, among other tools from information theory,…
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
In this work, our prime objective is to study the phenomena of quantum chaos and complexity in the machine learning dynamics of Quantum Neural Network (QNN). A Parameterized Quantum Circuits (PQCs) in the hybrid quantum-classical framework…
Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
Uncertainty relation usually is one of the most important features in quantum mechanics, and is the backbone of quantum theory, which distinguishes from the rule in classical counterpart. Specifically, entropy-based uncertainty relations…
We investigate the joint (separable) numerical range of multiple measurements, i.e., the regions of expectation values accessible with (separable) quantum states for given observables. This not only enables efficient entanglement detection,…