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We present a review and discussions on characterizations and quantifications of macroscopic quantum states as well as their implementations and applications in optical systems. We compare and criticize different measures proposed to define…
The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable -- a prominent example of the so-called quantum stochastic process -- fulfill the Kolmogorov consistency condition and thus…
Quantum correlations in a physical system are usually studied with respect to a unique (fixed) decomposition of the system into subsystems, without fully exploiting the rich structure of the state-space. Here, we show several examples in…
Deep insight can be gained into the nature of nonclassical correlations by studying the quantum operations that create them. Motivated by this we propose a measure of nonclassicality of a quantum operation utilizing the relative entropy to…
We propose to experimentally test the nonclassicality of quantum states through homodyne tomography. For single-mode states we check violations of inequalities involving the photon-number probability. For two-mode states we test the…
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. Our measure allows one to quantify coherence without having to perform tomography of the quantum state, and can be…
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies…
An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
One of the challenges in quantum information is the demonstration of quantum coherence in the operations of experimental devices. While full quantum process tomography can do the job, it is both cumbersome and unintuitive. In this…
Bosonic systems, particularly in quantum optics and atomic physics, are leading platforms for achieving quantum enhanced precision in parameter estimation. By exploiting properties such as mode and particle entanglement, it is possible to…
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…
The Fisher-Shannon statistical measure of complexity is analyzed for a continuous manifold of quantum observables. It is probed then than calculating it only in the configuration and momentum spaces will not give a complete description for…
In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…
A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation,…
Quantifying nonclassicality of a bosonic mode is an important but challenge task in quantum optics. Recently, the first nonclassicality measure based on the concept of operational resource theory has been proposed [Phys. Rev. Research 2,…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…