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The usual interpretational rule of quantum mechanics which states that outcomes do not occur when their weights are zero is changed so as to preclude outcomes with weights less than a small but positive value. With this "positive…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
The method of positive commutators, developed for zero temperature problems over the last twenty years, has been an essential tool in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive…
A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that…
We study the modified dynamical evolution of the neutral kaon system under the condition of complete positivity. The accuracy of the data from planned future experiments is expected to be sufficiently precise to test such a hypothesis.
We study the correlation dynamics of a system composed of arbitrary numbers of qutrits interacting with a common environment. Initially, the system is assumed to be in a low dimensional subspace of the Hamiltonian called "decoherence-free…
Can certain degrees of freedom of a closed physical system, described by a time-independent Hamiltonian, become more and more classical as they evolve from some state? This question is important because our universe seems to have done just…
A crucial goal of quantum information is to find new ways to exploit the properties of quantum devices as resources. One of the prominent properties of quantum devices of particular interest is their negativity in quasi-probability…
We study the stability of unitary quantum dynamics of composite systems (for example: central system + environment) with respect to weak interaction between the two parts. Unified theoretical formalism is applied to study different physical…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
The density matrix positivity is a natural counterpart of unitarity. The resulting constraints for various parton distribution and correlations are considered. Their compatibility with leading order QCD evolution is guaranteed by the…
We investigate the relationship between strict positivity of the Kossakowski matrix, irreducibility and positivity improvement properties of Markovian Quantum Dynamics. We show that for a Gaussian quantum dynamical semigroup strict…
Quantum information, in the form of entanglement with an ancilla, can be transmitted to a third system through interaction. Here, we investigate this process of entanglement transmission perturbatively in time. Using the entanglement…
We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic…
In order to better understand the structure of quantum theory, or speculate about theories that may supercede it, it can be helpful to consider alternative physical theories. ``Boxworld'' describes one such theory, in which all…
It has recently been shown that small quantum subsystems generically equilibrate, in the sense that they spend most of the time close to a fixed equilibrium state. This relies on just two assumptions: that the state is spread over many…
Positivity, the assumption that every unique combination of confounding variables that occurs in a population has a non-zero probability of an action, can be further delineated as deterministic positivity and stochastic positivity. Here, we…
In this note, we characterize the solution of a system of elliptic integro-differential equations describing a phe-notypically structured population subject to mutation, selection and migration. Generalizing an approach based on…
Darwinian evolution requires (i) heritable records, (ii) repeatable copying with variation, and (iii) routine irreversibility. Categorical quantum mechanics (CQM) makes precise why ``copy'' and ``delete'' are not generic quantum operations:…
The universe, as a closed system, is for all time in a state with a determinate value of energy, i.e., in an eigenstate of the Hamiltonian. That is the principle of cosmic energy determinacy. The Hamiltonian depends on cosmic time through…