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Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
Using the independent oscillator model with an arbitrary system potential, we derive a quantum Brownian equation assuming a correlated total initial state. Although not of Lindblad form, the equation preserves positivity of the density…
A general formlulation for discrete-time quantum mechanics, based on Feynman's method in ordinary quantum mechanics, is presented. It is shown that the ambiguities present in ordinary quantum mechanics (due to noncommutativity of the…
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:…
For quantum effects $a$ and $b$ we define the $a$-evolution of $b$ at time $t$ denoted by $b(t\mid a)$. We interpret $b(t\mid a)$ as the influence that $a$ has on $b$ at time $t$ when $a$ occurs, but is not measured at time $t=0$. Using…
We introduce a nonperturbative, first-principles approach to time-dependent problems in quantum field theory. In this approach, the time-evolution of quantum field configurations is calculated in real time and at the amplitude level. This…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
The role played by Time in the quantum theory is still mysterious by many aspects. In particular it is not clear today whether the distribution of decay times of unstable particles could be described by a Time Operator. As we shall discuss,…
We prove that, under suitable assumptions, operationally motivated data completely determine a space-time in which the quantum systems can be interpreted as evolving. At the same time, the dynamics of the quantum system is also determined.…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
We study the quantum evolution under the combined action of the exponentials of two not necessarily commuting operators. We consider the limit in which the two evolutions alternate at infinite frequency. This case appears in a plethora of…
A quasi-static process is realized in a purely quantum-mechanical model which is described by oscillator (or particle) systems having relative-phase interactions. Time development of a mixture of two oscillator (or particle) systems which…
For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as…
Assuming the validity of the equivalence principle in the quantum regime, we argue that one of the assumptions of the usual definition of quantum mechanics, namely separation between the ``classical'' detector and the ``quantum'' system,…
In quantum physics, measurements give random results and yield a corresponding random back action on the state of the system subject to measurement. If a quantum system is probed continuously over time, its state evolves along a stochastic…
One of the axioms of quantum field theory is the property of unitarity of the evolution operator. However, if one considers the quantum electrodynamics in the external field in the leading order of perturbation theory, one will find that…
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$…
With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…
We explore a possibility of measuring deviation from the exponential decay law in pure quantum systems. The power law behavior at late times of decay time profile is predicted in quantum mechanics, and has been experimentally attempted to…
We consider a quantum system strongly driven by forces that are periodic in time. The theorem concerns the probability $P(e)$ of observing a given energy change $e$ after a number of cycles. If the system is thermostated by a (quantum)…