Related papers: On the structure of covariant phase observables
In frameworks of the phenomenological approach we analyze of the phase diagram of mixed compounds. We obtain space groups of symmetry of the real structures as result of phase transition from close-packed degenerate structure. The theory of…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…
Simultaneous decoherence of conjugate observables of an open quantum system leads to a classical statistical mechanical description with constant phase space probability density in terms of a uniform ensemble. We investigate a scenario…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…
In this work we extend the Kugo-Ojima-Nakanishi covariant operator formalism to quantize two higher derivative systems, considering their extended phase space structures. More specifically, the one describing spin-$0$ particles by a vector…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
Classical sequential growth models for causal sets provide an important step towards the formulation of a quantum causal set dynamics. The covariant observables in a class of these models known as generalised percolation have been…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
In this work, a new class of vector-valued phase field models is presented, where the values of the phase parameters are constrained by a convex set. The generated phase fields feature the partition of the domain into patches of distinct…
Operators in quantum mechanics - either observables, density or evolution operators, unitary or not - can be represented by c-numbers in operator bases. The position and momentum bases are in one to one correspondence with lagrangian planes…
Phase plays a crucial role in many quantum effects including interference. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby…
We analyze the geometry on the space of non-unital phase-covariant qubit maps. Using the corresponding Choi-Jamio{\l}kowski states, we derive the Hilbert-Schmidt line and volume elements using the channel eigenvalues together with the…
We study various ways of characterising the quantum optical number and phase as complementary observables.
In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
We study an algebra spanned by modified Kostka polynomials. Particular structure coefficients of this algebra are interpreted as traces of some Weyl group actions on the intersection cohomology of comet-shaped quiver varieties.
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many…