Related papers: Quantum De Moivre-Laplace theorem for noninteracti…
We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a…
We study the nodal intersections number of random Gaussian toral Laplace eigenfunctions ("arithmetic random waves") against a fixed smooth reference curve. The expected intersection number is proportional to the the square root of the…
For a mixed quantum state with density matrix $\rho$ there are infinitely many ensembles of pure quantum states, which average to $\rho$. Starting from Laplace principle of insufficient reason (not to give \emph{a priori} preference to any…
We introduce a new family of probability distributions on the set of pure states of a finite dimensional quantum system. Without any a priori assumptions, the most natural measure on the set of pure state is the uniform (or Haar) measure.…
We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective…
Distinguishability theory is developed for quantum interference of the squeezed vacuum states on unitary linear interferometers. It is found that the entanglement of photon pairs over the Schmidt modes is one of the sources of…
In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This…
Cloning, or approximate cloning, is one of basic operations in quantum information processing. In this paper, we deal with cloning of classical states, or probability distribution in asymptotic setting. We study the quality of the…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
By a suitable shifting-the-mean parametrization at the Dirichlet series level and Delange's Tauberian theorems, we show that the number of factors in random ordered factorizations of integers is asymptotically normally distributed.
We consider the Riemannian random wave model of Gaussian linear combinations of Laplace eigenfunctions on a general compact Riemannian manifold. With probability one with respect to the Gaussian coefficients, we establish that, both for…
We consider the quantum expectation value \mathcal{A}=\<\psi|A|\psi\> of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all…
With the recent claim of a quantum advantage demonstration in photonics by Zhong et al, the question of the computation of lower-order approximations of boson sampling with arbitrary quantum states at arbitrary distinguishability has come…
The quantum theories of boson and fermion fields with quadratic nonstationary Hamiltoanians are rigorously constructed. The representation of the algebra of observables is given by the Hamiltonian diagonalization procedure. The sufficient…
In this paper I propose a new way for counting the microstates of a system out of equilibrium. As, according to quantum mechanics, things happen as if a given particle can be found in more than one state at once, I extend this concept to…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
Particle number fluctuations $N(t)$, measured in virtual observation boxes of an image or a simulation, offer a way to quantify particle dynamics when particle tracking is impractical, such as in high-density systems. While traditionally…
As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many…