Related papers: Tagged vector space, Part II: function space index…
In this Letter, we interpret the Husimi function as the conditional probability density of continuously measuring a stream of constant position and momentum outcomes, indefinitely. This gives rise to an alternative definition that naturally…
We analyze several product measures in the space of mixed quantum states. In particular we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a N x K…
We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-pace based quantum mutual coherence function is…
We investigate different geometries and invariant measures on the space of mixed Gaussian quan- tum states. We show that when the global purity of the state is held fixed, these measures coincide and it is possible, within this constraint,…
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…
This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum…
Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand…
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics…
The quantization of systems with first- and second-class constraints within the coherent-state path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral…
The partial trace operation is usually considered in composite quantum systems, to reduce the state on a single subsystem. This operation has a key role in the decoherence effect and quantum measurements. However, partial trace operations…
The notion of state vector is, in quantum mechanics, as central as it is problematic, as illustrates the wealth of publications about the sub- jects, including in particular the many attempts to obtain an acceptable interpretation of…
We provide formulae for the $\varepsilon$-subdifferential of the integral function $ I_f(x):=\int_T f(t,x) d\mu(t), $ where the integrand $f:T\times X \to [-\infty,+\infty]$ is measurable in $(t,x)$ and convex in $x$. The state variable…
We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thus, quantum mechanical systems are dissipatively embedded into a nonlinear classical dynamical structure. There is a…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
Gleason's theorem asserts the equivalence of von Neumann's density operator formalism of quantum mechanics and frame functions, which are functions on the pure states that sum to 1 on any orthonormal basis of Hilbert space of dimension at…
Repeated measurements can induce entanglement phase transitions in the dynamics of quantum systems. Interacting models, both chaotic and integrable, generically show a stable volume-law entangled phase at low measurement rates which…
Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, this definition has been generalized to such measures between…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can…
The quantum gravity problem of N point particles interacting with the gravitational field in 2+1 dimensions is approached working out the phase-space functional integral. The maximally slicing gauge is adopted for a non compact open…