Related papers: Quantum Weakest Preconditions
We investigate four key issues with using a nonzero weak value of the spatial projection operator to infer the past path of an individual quantum particle. First, we note that weak measurements disturb a system, so any approach relying on…
The necessity and utility of considering the interaction of a quantum system with its environment when describing its time evolution have been recognized in several branches of physics and of other sciences. The Kraus' representation is a…
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of…
We propose terminology to classify interpretations of quantum mechanics and models that modify or complete quantum mechanics. Our focus is on models which have previously been referred to as superdeterministic (strong or weak), retrocausal…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
Continuity is one of the most central notions in mathematics, physics, and computer science. An interesting associated topic is decompositions of continuity, where continuity is shown to be equivalent to the combination of two or more weak…
We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak…
Modeling hydrological fracture networks is a hallmark challenge in computational earth sciences. Accurately predicting critical features of fracture systems, e.g. percolation, can require solving large linear systems far beyond current or…
We show the Standard Model and SuperString Theories can be naturally based on a Quantum Computer foundation. The Standard Model of elementary particles can be viewed as defining a Quantum Computer Grammar and language. A Quantum Computer in…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
We introduce the notions of quantum characteristic and quantum flatness for arbitrary rings. More generally, we develop the theory of quantum integers in a ring and show that the hypothesis of quantum flatness together with positive quantum…
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a…
The word \textit{proposition} is used in physics with different meanings, which must be distinguished to avoid interpretational problems. We construct two languages $\mathcal{L}^{\ast}(x)$ and $\mathcal{L}(x)$ with classical set-theoretical…
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and…
In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for…
Quantum kernel methods are a proposal for achieving quantum computational advantage in machine learning. They are based on a hybrid classical-quantum computation where a function called the quantum kernel is estimated by a quantum device…
Quantum operations are the most widely used tool in the theory of quantum information processing, representing elementary transformations of quantum states that are composed to form complex quantum circuits. The class of quantum…
The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance. This…
We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias…
The failure of distributivity in quantum logic is motivated by the principle of quantum superposition. However, this principle can be encoded differently, i.e., in different logico-algebraic objects. As a result, the logic of experimental…