Related papers: On the structure of non-commutative white noises
Several long-time limit theorems of one-dimensional L\'evy processes weighted and normalized by functions of its supremum are studied. The long-time limits are taken via the families of exponential times and that of constant times, called…
In this paper, we present a Hamiltonian identification method for a closed quantum system whose time trace observables are measured with colored measurement noise. The dynamics of the quantum system are described by a Liouville equation…
Current quantum technologies are at the cusp of becoming useful, but still face formidable obstacles such as noise. Noise severely limits the ability to scale quantum devices to the point that they would offer an advantage over classical…
We study the growth properties of the family of i.i.d. random sequences, also known as discrete white noises, and of their continuous-domain generalization, the family of L\'evy white noises. More precisely, we characterize the members of…
Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the…
We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to…
Quantum systems are unavoidably open to their surrounding degrees of freedom. The theory of open quantum systems is thus crucial to understanding the fluctuations, dissipation, and decoherence of a quantum system of interest. Typically, the…
This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…
In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. A special inequality which…
We discuss three different aspects of the quantum dynamics of bio-molecular systems and more generally complex networks in the presence of strongly coupled environments. Firstly, we make a case for the systematic study of fundamental…
We develop a structure theory for decoherence-free subspaces and noiseless subsystems that applies to arbitrary (not necessarily unital) quantum operations. The theory can be alternatively phrased in terms of the superoperator perspective,…
We present a canonical formalism for computing quantum fluctuations of certain discrete degrees of freedom in systems governed by integrable partial differential equations with known Hamiltonian structure, provided these models are…
I show that when non-linearities are taken into account the Landau theory of Fermi liquids predicts the existence of hyperbolic waves in fermionic systems. The zero sound is described by a infinite set of coupled non-linear partial…
The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of…
Dynamical systems driven by a general L\'evy stable noise are considered. The inertia is included and the noise, represented by a generalised Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time-dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional…
We accurately characterize nonlinear phase noise in uncompensated coherent optical systems. We find that, though present, its impact on system performance is typically negligible in a wide range of practical system scenarios.
The non-classical nature of quantum states, often illustrated using entanglement measures or quantum discord, constitutes a resource for quantum information protocols. However, the non-classicality of a quantum system cannot be encapsulated…
Among quantum Langevin equations describing the unitary time evolution of a quantum system in contact with a quantum bath, we completely characterize those equations which are actually driven by classical noises. The characterization is…