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Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…
We give a description of the teleportation of an unknown quantum state which takes into account the action of the measuring device and manifestly avoids any reference to the postulate of the state vector collapse.
A new approach suitable for distributed quantum machine learning and exhibiting memory is proposed for a photonic platform. This measurement-based quantum reservoir computing takes advantage of continuous variable cluster states as the main…
The measurement procedures used in quantum teleportation are analyzed from the viewpoint of the general theory of quantum-mechanical measurements. It is shown that to find the teleported state one should only know the identity resolution…
Quantum operations arise naturally in many fields of quantum information theory and quantum computing. One of the simplest example of quantum operation is the von Neumann-Lueders measurement. Destruction of states in quantum mechanics can…
Two theorems with applications to the quantum theory of measurements are stated and proven. The first one clarifies and amends von Neumann's Measurement Postulate used in the Copenhagen interpretation of quantum mechanics. The second one…
Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines and fridges to power plants and solar cells. With thermodynamics predating…
The determination of the quantum state of a single system by protective observation is used to justify operationally a formulation of quantum theory on the quantum state space (projective Hilbert space) $\cal P$. Protective observation is…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two spatially separated and noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements…
A history of the discovery of quantum mechanics and paradoxes of its interpretation is reconsidered from the modern point of view of quantum stochastics and information. It is argued that in the orthodox quantum mechanics there is no place…
A measurement on a macroscopic quantum system does in general not lead to a projection of the wavefunction in the basis of the detector as predicted by von-Neumann's postulate. Hence, it is a question of fundametal interest, how the…
It is argued that Feynman's rules for evaluating probabilities, combined with von Neumann's principle of psycho-physical parallelism, help avoid inconsistencies, often associated with quantum theory. The former allows one to assign…
This work develops a conceptual framework for the foundations of quantum physics, linking two main approaches: the algebraic formulation and quantum probability. Rather than proposing new axioms or theories, the text reorganizes and…
In this paper, I attempt a personal account of my understanding of the measurement problem in quantum mechanics, which has been largely in the tradition of the Copenhagen interpretation. I assume that (i) the quantum state is a…
In recent results, it has been proven that all sampling methods produce outliers. In this paper, we extend these results to quantum information theory. Projectors of large rank must contain pure quantum states in their images that are…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…