Related papers: Quantum dynamical entropy, chaotic unitaries and c…
The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of…
We propose a phase-space Wigner harmonics entropy measure for many-body quantum dynamical complexity. This measure, which reduces to the well known measure of complexity in classical systems and which is valid for both pure and mixed states…
The theoretical description of quantum dynamics in an intriguing way does not necessarily imply the underlying dynamics is indeed intriguing. Here we show how a known very interesting master equation with an always negative decay rate…
We study how dynamical quantities such as Lyapunov exponents, metric entropy, topological pressure, recurrence rates, and dimension-like characteristics change under a time reparameterization of a dynamical system. These quantities are…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
We study the behavior of a quantum particle trapped in a confining potential in one dimension under multiple sudden changes of velocity and/or acceleration. We develop the appropriate formalism to deal with such situation and we use it to…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
Local parametric statistics of zeros of Husimi representations of quantum eigenstates are introduced. It is conjectured that for a classically fully chaotic systems one should use the model of parametric statistics of complex roots of…
For the 1-D harmonic oscillator with position depending variable mass, a Hamiltonian and constant of motion are given through a consistent approach. Then, the quantization of this system is carried out using the operator $\hat p$, for the…
We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of the…
We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a…
A continuously monitored quantum bit (qubit) exhibits competition between unitary Hamiltonian dynamics and non-unitary measurement-collapse dynamics, which for diffusive measurements form an enlarged transformation group equivalent to the…
We address the problem of continuous-variable quantum phase estimation in the presence of linear disturbance at the Hamiltonian level, by means of Gaussian probe states. In particular we discuss both unitary and random disturbance, by…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
Mean-field systems provide a natural framework in which collective effects persist as the number of degrees of freedom N increases, raising fundamental questions about the emergence of integrability and the nature of chaos in large but…
Programmable quantum devices provide a platform to control the coherent dynamics of quantum wavefunctions. Here we experimentally realize adaptive monitored quantum circuits, which incorporate conditional feedback into non-unitary…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…