Related papers: Probability Measures and projections on Quantum Lo…
We assume that M is a phase space and H an Hilbert space yielded by a quantization scheme. In this paper we consider the set of all "experimental propositions" of M and we look for a model of quantum logic in relation to the quantization of…
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
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…
Relational verification of quantum programs has many potential applications in quantum and post-quantum security and other domains. We propose a relational program logic for quantum programs. The interpretation of our logic is based on a…
Quantum mechanical weak values of projection operators have been used to answer which-way questions, e.g. to trace which arms in a multiple Mach-Zehnder setup a particle may have traversed from a given initial to a prescribed final state. I…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
Quantum Mechanics (QM) predicts the correlation between measurements performed in remote regions of a spatially spread entangled state to be higher than allowed by the intuitive concepts of Locality and Realism (LR). This high correlation…
Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually…
This paper shows how inference is treated within the context of Eigenlogic projection operators in linear algebra. In Eigenlogic operators represent logical connectives, their eigenvalues the truth-values and the associated eigenvectors the…
This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic…
Quantum mechanics does not permit joint measurements of non-commuting observables. However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property. The results can be…
We present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the…
In this paper we attempt to analyze the concept of quantum probability within quantum computation and quantum computational logic. While the subjectivist interpretation of quantum probability explains it as a reliable predictive tool for an…
The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably…
We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries…
The predictions of quantum mechanics cannot be resolved with a completely classical view of the world. In particular, the statistics of space-like separated measurements on entangled quantum systems violate a Bell inequality. We put forward…
Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these `lattice spacing' weights do not have to be independent of the direction of the arrow. We use this…
We define an index of compatibility for a probabilistic theory (PT). Quantum mechanics with index 0 and classical probability theory with index 1 are at the two extremes. In this way, quantum mechanics is at least as incompatible as any PT.…
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but…
Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess…