Related papers: (Un)decidable Problems about Reachability of Quant…
The quest to identify quantum advantages lies at the heart of quantum technology. While quantum devices promise extraordinary capabilities, from exponential computational speedups to unprecedented measurement precision, distinguishing…
Quantum mechanics is already 100 years old, but remains alive and full of challenging open problems. On one hand, the problems encountered at the frontiers of modern theoretical physics like Quantum Gravity, String Theories, etc. concern…
The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this…
We study the qualitative and quantitative zero-reachability problem in probabilistic multi-counter systems. We identify the undecidable variants of the problems, and then we concentrate on the remaining two cases. In the first case, when we…
We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
A quantum mechanical system S is indirectly controlled when the control affects an ancillary system A and the evolution of S is modified through the interaction with A only. A study of indirect controllability gives a description of the set…
Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one…
A major challenge to the control of infinite dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space…
The problem investigated in this paper is einselection, i. e. the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection…
It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
This paper provides a framework for the control of quantum mechanical systems with scattering states, i.e., systems with continuous spectra. We present the concept and prove a criterion of the approximate strong smooth controllability. Our…
The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set $\cal A$ of operationally relevant observables. The algebraic structure of $\cal A$ selects a preferred tensor product…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…
In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an…
A complete deterministic finite (semi)automaton (DFA) with a set of states $Q$ is \emph{completely reachable} if every nonempty subset of $Q$ is the image of the action of some word applied to $Q$. The concept of completely reachable…
We introduce a Markov chain model of concurrent quantum programs. This model is a quantum generalization of Hart, Sharir and Pnueli's probabilistic concurrent programs. Some characterizations of the reachable space, uniformly repeatedly…
Quantum systems prepared in pure states evolve into mixtures under environmental action. Physically realizable ensembles are the pure state decompositions of those mixtures that can be generated in time through continuous measurements of…