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Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics defining a…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
In arXiv:0709.0483 Gunther and Samsonov outline a ``generalization'' of quantum mechanics that involves simultaneous consideration of Hermitian and non-Hermitian operators and promises to be ``capable to produce effects beyond those of…
Quantum measurement is a fundamental concept in the field of quantum mechanics. The action of quantum measurement, leading the superposition state of the measured quantum system into a definite output state, not only reconciles…
Although quantum mechanics is a mature theory, fundamental problems discussed during its time of foundation have remained with us to this day. These problems are centered on the problematic relation between the quantum and classical worlds.…
Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise…
$P$-divisibility is a central concept in both classical and quantum non-Markovian processes; in particular, it is strictly related to the notion of information backflow. When restricted to a fixed commutative algebra generated by a complete…
This paper discusses the relation between the decoherent histories approach to quantum mechanics that is based on coarse-grained decoherent histories of a closed system, and the approximate quantum mechanics of measured subsystems, as in…
A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating…
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…
Consecutive quantum measurements performed on the same system can reveal fundamental insights into quantum theory's causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic…
Correlations between spacelike separated measurements on entangled quantum systems are stronger than any classical correlations and are at the heart of numerous quantum technologies. In practice, however, spacelike separation is often not…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
Quantum coherence and quantum correlations lie in the center of quantum information science, since they both are considered as fundamental reasons for significant features of quantum mechanics different from classical mechanics. We present…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
Quantum theory depends on an external classical time, and there ought to exist an equivalent reformulation of the theory which does not depend on such a time. The demand for the existence of such a reformulation suggests that quantum theory…
In the classical world one can construct two identical systems which have identical behavior and give identical measurement results. We show this to be impossible in the quantum domain. We prove that after the same quantum measurement two…
The origin of the uncertainty inherent in quantum measurements has been discussed since quantum theory's inception, but to date the source of the indeterminacy of measurements performed at an angle with respect to a quantum state's…
The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that operational prescriptions, which are integral to experimental physics,…