Related papers: Record statistics in random vectors and quantum ch…
We address the theory of records for integrated random walks with finite variance. The long-time continuum limit of these walks is a non-Markov process known as the random acceleration process or the integral of Brownian motion. In this…
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…
The statistics of records for a time series generated by a continuous time random walk is studied, and found to be independent of the details of the jump length distribution, as long as the latter is continuous and symmetric. However, the…
In quantum operations, probabilities characterise both the degree of the success of a state transformation and, as density operator eigenvalues, the degree of mixedness of the final state. We give a unified treatment of pure-to-pure state…
A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a L\'evy flight on a line. After a brief survey of the theory of records for independent and…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
The characterization of record events is considered for a discrete-time random walk model with long-term memory arising from correlations between successive steps. An important feature is that the correlations are strong enough to give rise…
In this work, Bernoulli's Law of Large Numbers, also known as the Golden theorem, has been extended to study the relations between empirical probability and empirical randomness of an otherwise random experiment. Using the example of a coin…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here,…
Recently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. The latter refers to a sudden change in a…
The analysis of a continuous measurement record $z(t)$ poses a fundamental challenge in quantum measurement theory. Different approaches have been used in the past as records can, e.g., exhibit predominantly Gaussian noise, telegraph noise,…
The quantum fluctuations of a physical property can be observed in the measurement statistics of any measurement that is at least partially sensitive to that physical property. Quantum theory indicates that the effective distribution of…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
Non-equilibrium dynamics of many-body quantum systems under the effect of measurement protocols is attracting an increasing amount of attention. It has been recently revealed that measurements may induce different non-equilibrium regimes…
The unpredictable process of state collapse caused by quantum measurements makes the generation of quantum randomness possible. In this paper, we explore the quantitive connection between the randomness generation and the state collapse and…
Quantum information processing shows advantages in many tasks, including quantum communication and computation, comparing to its classical counterpart. The essence of quantum processing lies on the fundamental difference between classical…
The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate…
A theoretical analysis of the statistical distributions of the reflected intensities from random media is presented. We use random matrix theory to analytically deduce the probability densities in the localization regime. Numerical…