Related papers: Approximating macroscopic observables in quantum s…
A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not…
Mutually Unbiased Bases (MUBs) are closely connected with quantum physics, and the structure has a rich mathematical background. We provide equivalent criteria for extending a set of MUBs for $C^n$ by studying real points of a certain…
In quantum measurement theory, a measurement scheme describes how an observable of a given system can be measured indirectly using a probe. The measurement scheme involves the specification of a probe theory, an initial probe state, a probe…
We investigate the non-equilibrium dynamics of isolated quantum spin systems via an exact mapping to classical stochastic differential equations. We show that one can address significantly larger system sizes than recently obtained,…
We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution…
The fluctuations are termed mesoscopic, when their typical size is essentially larger then the average distance between the nearest neighbors, while being much smaller than the overall system size. Since the features of mesoscopic…
Quantum systems allow one to sense physical parameters beyond the reach of classical statistics---with resolutions greater than $1/N$, where $N$ is the number of constituent particles independently probing a parameter. In the canonical…
For a sufficiently nice 2 dimensional shape, we define its approximating matrix (or patterned matrix) as a random matrix with iid entries arranged according to a given pattern. For large approximating matrices, we observe that the…
System of 1/2 spin particles is observed repeatedly using Stern-Gerlach apparatuses with rotated orientations. Synthesis of such non-commuting observables is analyzed using maximum likelihood estimation as an example of quantum state…
In this work, we develop a mathematical framework to model a quantum system whose Hamiltonian may depend on the state of changing environment, that evolves according to a Markovian process. When the environment changes its state, the…
This note presents a canonical construction of global observables -- sometimes referred to in the literature as macroscopic observables or observables at infinity -- in statistical mechanics, providing a unified treatment of both…
Simultaneous measurement of several noncommuting observables is modeled by using semigroups of completely positive maps on an algebra with a non-trivial center. The resulting piecewise-deterministic dynamics leads to chaos and to nonlinear…
We study conditions for the existence of asymptotic observables in cosmology. With the exception of de Sitter space, the thermal properties of accelerating universes permit arbitrarily long observations, and guarantee the production of…
In physical experiments, reference frames are standardly modelled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical…
Macroscopic quantum phenomena refer to quantum features in objects of `large' sizes, systems with many components or degrees of freedom, organized in ways where they can be identified as macroscopic objects. This emerging field is ushered…
A model quantum system is proposed to describe position states of a massive body in flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators,…
We compute the asymptotics of matrix elements in canonical bases of irreducible representations of the unitary group as the highest weight goes to infinity, in terms of the symplectic geometry of the associated coadjoint orbit. This uses…
Unsharp spin observables are shown to arise from the fact that a residual uncertainty about the actual alignment of the measurement device remains. If the uncertainty is below a certain level, and if the distribution misalignments is…
The interaction between an ultrarelativistic particle and a linear array made up of $N$ two-level systems (^^ ^^ AgBr" molecules) is studied by making use of a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…