Related papers: Quantum theory realises all joint measurability gr…
Quantum theory is incredibly successful, explaining the microscopic world with great accuracy, from the behaviour of subatomic particles to chemical reactions to solid-state electronics. There is not a single experimental finding…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…
Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…
Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
The incompatibility of measurements is the key feature of quantum theory that distinguishes it from the classical description of nature. Here, we consider groups of d-outcome quantum observables with prime d represented by non-Hermitian…
We establish a quantum version of Frucht's Theorem, proving that every finite quantum group is the quantum automorphism group of an undirected finite quantum graph. The construction is based on first considering several quantum Cayley…
Maximum likelihood principle is shown to be the best measure for relating the experimental data with the predictions of quantum theory.
This paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information.…
The measurement process is considered for quantum field theory on curved spacetimes. Measurements are carried out on one QFT, the "system", using another, the "probe" via a dynamical coupling of "system" and "probe" in a bounded spacetime…
The main obstacle in attempts to construct a consistent quantum gravity is the absence of independent flat time. This can in principle be cured by going out to higher dimensions. The modern paradigm assumes that the fundamental theory of…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
We formalize the quantum arithmetic, i.e. a relationship between number theory and operator algebras. Namely, it is proved that rational projective varieties are dual to the $C^*$-algebras with real multiplication. Our construction fits all…
The notion of incompatibility of measurements in quantum theory is in stark contrast with the corresponding classical perspective, where all physical observables are jointly measurable. It is of interest to examine if the results of two or…
In order to prevent ``unavoidable'' break-down of the ``peaceful coexistence'' between foundations of quantum theory and relativity I propose a new type of a quantum gauge theory (superrelativity). This differs from ordinary gauge theories…
Witten described how a path integral quantization of Wilson Loop observables will define Jones polynomial type of link invariants, using the Chern-Simons gauge theory in $\mathbb{R}^3$. In this gauge theory, a compact Lie group ${\rm G}$,…
The theory of positive maps plays a central role in operator algebras and functional analysis, and has countless applications in quantum information science. The theory was originally developed for operators acting on complex Hilbert…
Recently a study of the first superposed mechanical quantum object ("machine") visible to the naked eye was published. However, as we show, it turns out that if the object would actually be observed, i.e. would interact with an optical…
We clarify the correspondence between the two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side…