Related papers: Remarks on the notion of quantum integrability
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.
On the basis of a manifestly covariant formalism of non-relativistic quantum mechanics in general coordinate systems, proposed by us recently, we derive general expressions for inertial forces. The results enable us further to discuss, and…
The quantum mechanical measurement process is considered. A hypothetical concept of irrational dynamical variables is proposed. A possible definition of measurement is discussed along with a mathematical method to calculate experimental…
It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of…
Quantum mechanics, the fundamental theory that governs the behaviour of matter and energy at microscopic scales, forms the foundation of quantum computing and quantum information science. As quantum technologies progress, software engineers…
The development of estimation and control theories for quantum systems is a fundamental task for practical quantum technology. This vision article presents a brief introduction to challenging problems and potential opportunities in the…
Modelling quantum devices is to find a model according to quantum theory that can explain the result of experiments in a quantum device. We find that usually we cannot correctly identify the model describing the actual physics of the device…
We explore a wider theoretical framework that has quantum field theory built-in, taking the fact that quantum mechanics is reconstructed from quantum field theory as a hint. We formulate a quantum theory with an embedded structure by…
The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. Of particular practical relevance…
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss…
The characterization of the quantum ensemble is a fundamental issue in quantum information theory and foundations. The ensemble is also useful for various quantum information processing. To characterize the quantum ensemble, in this…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
In this paper we introduce the notion of admissible skein modules associated to an ideal in a pivotal category. We explain how these modules are generalizations of the Kauffman skein algebra and how they relate to renormalized quantum…
We reconsider some important foundational problems of quantum mechanics. After reviewing the measurement problem and discussing its unavoidability, we analyze some proposals to overcome it. This analysis leads us to reconsider the current…
A phase space mathematical formulation of quantum mechanical processes accompanied by and ontological interpretation is presented in an axiomatic form. The problem of quantum measurement, including that of quantum state filtering, is…
I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the "measurement problem") could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before…
In this paper we are going to introduce a new dynamical postulate in Quantum Mechanics. This new principle is defined using path integrals over the set of normalized wave functions. We will show in a qualitative way that this postulate is…
Modern quantum engineering techniques enabled successful foundational tests of quantum mechanics. Yet, the universal validity of quantum postulates is an open question. Here we propose a new theoretical framework of Q-data tests, which…
The conceptual problems in quantum mechanics -- related to the collapse of the wave function, the particle-wave duality, the meaning of measurement -- arise from the need to ascribe particle character to the wave function. As will be shown,…
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…