Related papers: Remarks on quantum transmutation
The quantum singular value transformation has revolutionised quantum algorithms. By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms. However, polynomials are restricted to definite parity…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…
Transition probabilities are an important and useful tool in quantum mechanics. However, in their present form, they are limited in scope and only apply to pure quantum states. In this article we extend their applicability to mixed states…
It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the…
We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the `atomic version'. We then review some…
We give a new sufficient condition on a spectral triple to ensure that the quantum group of orientation and volume preserving isometries defined in \cite{qorient} has a $C^*$-action on the underlying $C^*$ algebra.
In this paper, we study generalized quantum operations and almost sharp quantum effects, our results generalize and improve some important conclusions in [2] and [3].
Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. In this letter we present a general method based on quantum tomography for…
A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the G\^ateaux derivative or commutators. This…
The final version of a new approach to quantum theory is formulated in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to…
We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our…
A new notation has been introduced for the quantum information theory. By this notation,some calculations became simple in quantum information theory such as quantum swapping, quantum teleportation.
In this work we take a closer look at the algebraic-operator correspondence between the momentum space and the position space which defines the form of the canonical momentum operator in position space in Quantum Mechanics (QM). Starting…
The concept of quantum commutativity with respect to an action or coaction of a given Hopf algebra is used for the algebraic description of a system of particles and their interaction with certain quantum field. Graded commutativity and…
We present a group of transformations in the quantum configuration space of loop quantum gravity that contains the set of all transformations generated by the flux variables.
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
We present a general algorithm, based on machine learning, which can create optimal unitary operators to implement quantum teleportation in any system with well-defined set of measurements in a relevant entangled basis. We illustrate it…
We present some informal remarks on aspects of relativistic quantum computing.
We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance.