Related papers: On the relation between transformation dynamics an…

The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the…

We derive schemes to measure the so-called weak values of quantum system observables by coupling of the system to a qubit meter system. We highlight, in particular, the meaning of the imaginary part of the weak values, and show how it can…

We first introduce the concept of weak random periodic solutions of random dynamical systems. Then, we discuss the existence of such periodic solutions. Further, we introduce the definition of weak random periodic measures and study their…

In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature…

After surveying the quantum kinematics and dynamics of statistical transmutation, I show how this concept suggests a phase diagram for the two-dimensional matter in a magnetic field, as a function of quantum statistics. I discuss the…

This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…

We generalize the concept of a weak value of a quantum observable to cover arbitrary real positive operator measures. We show that the definition is operationally meaningful in the sense that it can be understood within the quantum theory…

We consider the concept of statistical complexity to write the quasiperiodical damped systems applying the snapshot attractors. This allows us to understand the behaviour of these dynamical systems by the probability distribution of the…

Weak measurements are a new tool for characterizing post-selected quantum systems during their evolution. Weak measurement was originally formulated in terms of von Neumann interactions which are practically available for only the simplest…

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…

Dynamical quantum phase transitions (DQPTs) occur at times when a quantum state exhibits a nonanalytic change in its return probability. This can be viewed as the probability of collapsing the evolved state to the initial state by quantum…

Statistical paradoxes such as the Hardy paradox and the enhancement of phase estimation via post-selection both draw upon the same non-classical features of quantum statistics described by non-positive quasi-probabilities. In this paper, we…

In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…

The problem of feedback control of quantum systems by means of weak measurements is investigated in detail. When weak measurements are made on a set of identical quantum systems, the single-system density matrix can be determined to a high…

One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known…

We study trade-off relations in information extraction from quantum systems subject to null-result weak measurements, where the absence of a detected photon continuously updates the system state. We present a detailed analysis of qubit and…

We describe some applications of quantum information theory to the analysis of quantum limits on measurement sensitivity. A measurement of a weak force acting on a quantum system is a determination of a classical parameter appearing in the…

Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental. In fact, quantum states are merely summaries of dynamical processes that randomize the properties of the…

Weak values are typically obtained experimentally by performing weak measurements, which involve weak interactions between the measured system and a probe. However, the determination of weak values does not necessarily require weak…

The weak value, the average result of a weak measurement, has proven useful for probing quantum and classical systems. Examples include the amplification of small signals, investigating quantum paradoxes, and elucidating fundamental quantum…