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Generalised quantum measurements go beyond the textbook concept of a projection onto an orthonormal basis in Hilbert space. They are not only of fundamental relevance but have also an important role in quantum information tasks. However, it…
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…
Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system…
In this work, we reveal a new type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any non-trivial threshold in a perfect or an unambiguous way. This…
We study the probabilistic consequences of the choice of the basic number field in quantum formalism. We demonstrate that by choosing a number field for a linear space representation of quantum model it is possible to describe various…
People are witnessing quantum computing revolutions nowadays. Progress in the number of qubits, coherence times and gate fidelities are happening. Although quantum error correction era has not arrived, the research and development of…
Bohr's complementarity principle is of fundamental historic and conceptual importance for Quantum Mechanics (QM), and states that, with a given experimental apparatus configuration, one can observe either the wave-like or the particle-like…
Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
One of the fundamental theories of physics is that of quantum mechanics. Quantum mechanics tries to explain the inconsistencies in the behaviors of systems at the macro and micro scales. Quantum mechanics paved the way for quantum computing…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
Quantum mechanics of unitary systems is considered in quasi-Hermitian representation. In this framework the concept of perturbation is found counterintuitive, for three reasons. The first one is that in this formalism we are allowed to…
I explore the possibility that a quantum system S may be described completely by the combination of its standard quantum state $|\psi\rangle$ and a (hidden) quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that the…
In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the…
We discuss the Mellin-Barnes representation of complex multidimensional integrals. Experiments frontiered by the High-Luminosity Large Hadron Collider at CERN and future collider projects demand the development of computational methods to…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are…