Related papers: Probability sum rules and consistent quantum histo…
The possibility of consistency between the basic quantum principles of quantum mechanics and wave function collapse is reexamined. A specific interpretation of environment is proposed for this aim and applied to decoherence. When the…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
The physical meaning of weak values and measurements can be completely understood with Born rule and the general probability theory. It is known that the weak value of an observable $\hat A$ with post-selection $\langle F|$ may be out of…
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion of the resource. Here we solve this…
The subjective Bayesian interpretation of probability asserts that the rules of the probability calculus follow from the normative principle of Dutch-book coherence: A decision-making agent should not assign probabilities such that a series…
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when…
We report on the effects of a simple decoherence model on the quantum search algorithm. Despite its simplicity, the decoherence model is an instructive model that can genuinely imitate realistic noisy environment in many situations. As one…
By using relative entropy of coherence, we characterize the coherence gain induced by some quantum evolutions, including the cohering power of unitary operations and the decohering power of quantum operations. We find that the cohering…
A number of phenomena generally believed characteristic of quantum mechanics and seen as interpretively problematic--the incompatibility and value-indeterminacy of variables, the non-existence of dispersion-free states, the failure of the…
A while loop tests a termination condition on every iteration. On a quantum computer, such measurements perturb the evolution of the algorithm. We define a while loop primitive using weak measurements, offering a trade-off between the…
We consider decoherence of quantum registers, which consist of the qubits sited approximately periodically in space. The sites of the qubits are permitted to have a small random variance. We derive the explicit conditions under which the…
In this universe, governed fundamentally by quantum mechanical laws, characterized by indeterminism and distributed probabilities, classical deterministic laws are applicable over a wide range of time, place, and scale. We review the origin…
A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence $\Xi$, and discuss in some detail a general…
We review recent progress in understanding the arrival time problem in quantum mechanics, from the point of view of the decoherent histories approach to quantum theory. We begin by discussing the arrival time problem, focussing in…
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can…
Despite the fact that we have some proposals for the quantum theory of gravity like string theory or loop quantum gravity, we do not have any experimental evidence supporting any of these theories. Actually, we do not have experimental…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
We consider the effect of different unitary noise mechanisms on the evolution of a quantum walk (QW) on a linear chain with a generic coin operation: (i) bit-flip channel noise, restricted to the coin subspace of the QW, and (ii)…
Many probabilistic programming languages allow programs to be run under constraints in order to carry out Bayesian inference. Running programs under constraints could enable other uses such as rare event simulation and probabilistic…