Related papers: Quantum Markov Order
Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show…
An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations…
In the current era of noisy intermediate-scale quantum (NISQ) devices, research in the theory of open system dynamics has a crucial role to play. In particular, understanding and quantifying memory effects in quantum systems is critical to…
The paradigm of considering open quantum systems -- i.e. focusing only on the system of interest, and treating the rest of the world as an effective environment -- has proven to be a highly effective way to understand a range of quantum…
Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly…
In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of…
Recently, a series of different measures quantifying memory effects in the quantum dynamics of open systems has been proposed. Here, we derive a mathematical representation for the non-Markovianity measure based on the exchange of…
Recently, as an aid for musical analysis, in computational musicology mathematical and informatics tools have been developed to quantitatively characterize some aspects of musical compositions. To a musical composition can be attributed by…
Stochastic processes abound in nature and accurately modeling them is essential across the quantitative sciences. They can be described by hidden Markov models (HMMs) or by their quantum extensions (QHMMs). These models explain and give…
The concept of quantum-mechanical nematic order, which is important in systems such as superconductors, is based on an analogy to classical liquid crystals, where order parameters are obtained through orientational expansions. We generalize…
We analyze recent approaches to quantum Markovianity and how they relate to the proper definition of quantum memory. We point out that the well-known criterion of information backflow may not correctly report character of the memory falsely…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…
The non-Markovian nature of open quantum dynamics lies in the structure of the multitime correlations, which are accessible by means of interventions. Here, by examining multitime correlations, we show that it is possible to engineer…
We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable -- a prominent example of the so-called quantum stochastic process -- fulfill the Kolmogorov consistency condition and thus…
A Markovian process of a system is defined classically as a process in which the future state of the system is fully determined by only its present state, not by its previous history. There have been several measures of non-Markovianity to…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…
Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is…
Generic open quantum dynamics can be described by two seemingly very distinct approaches: a top down approach by considering an (unknown) environment coupled to the system and affects the observed dynamics of the system; or a bottom up…