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Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum…
The key to optical analogy to a multi-particle quantum system is the scalable property. Optical elds modulated with pseudorandom phase sequences is an interesting solution. By utilizing the properties of pseudorandom sequences, mixing…
We consider the problem of representation of quantum states and observables in the framework of classical probability theory (Kolmogorov's measure-theoretic axiomatics, 1933). Our aim is to show that, in spite of the common opinion,…
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is…
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for some realistic models with hidden variables. There are, however, two powerful theorems…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
Quantum features of correlated optical modes define a major aspect of the nonclassicality in quantized radiation fields. However, the phase-sensitive detection of a two-mode light field is restricted to interferometric setups and local…
A state of a quantum systems can be regarded as {\it classical} ({\it quantum}) with respect to measurements of a set of canonical observables iff there exists (does not exist) a well defined, positive phase space distribution, the so…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum and definite…
The conceptual problems in quantum mechanics -- related to the collapse of the wave function, the particle-wave duality, the meaning of measurement -- arise from the need to ascribe particle character to the wave function. As will be shown,…
The emerging field of entanglement or nonseparability in classical optics is reviewed, and its similarities with and differences from quantum entanglement clearly pointed out through a recapitulation of Hilbert spaces in general, the…
We are concerned with numerical simulations of quantum optical circuits under certain realistic conditions, specifically that photon quantum states are not perfectly indistinguishable. The partial photon distinguishability presents a…
We address nonsequential double ionization induced by strong, linearly polarized laser fields of only a few cycles, considering a physical mechanism in which the second electron is dislodged by the inelastic collision of the first electron…
Experimentally observed violations of Bell inequalities rule out local realistic theories. Consequently, the quantum state vector becomes a strong candidate for providing an objective picture of reality. However, such an ontological view of…
Fundamental principle of classical physics -- local realism, means that freely chosen observations can be explained by a local (slower than light) real process. It is apparently violated in quantum mechanics as shown by Bell theorem.…
In the first part of this thesis Bell's theorem is revisited. It points at a difference between the quantum and the classical world. This difference is often behind the advantages of solutions using quantum mechanics. New and more general…
We propose a legitimate and easily computable nonclassicality indicator for the states of electromagnetic fields based on the standard deviation in the measurement of the homodyne rotated quadrature operator. The proposed nonclassicality…
In contrast with classical physics, in quantum physics some sets of measurements are incompatible in the sense that they can not be performed simultaneously. Among other applications, incompatibility allows for contextuality and Bell…
For linear combinations of quantum product averages in an arbitrary bipartite state, we derive new quantum Bell-form and CHSH-form inequalities with the right-hand sides expressed in terms of a bipartite state. This allows us to specify in…