Related papers: Dimensions, nodes and phases in quantum numbers
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination,…
The quantum world is fascinating. It presents a description of nature that defies our most rooted concepts about what reality is. For example, quantum objects possess \lq\lq spooky\rq\rq\ properties that allow them to be in multiple places…
If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can…
There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical…
Merging disciplines has led to incredible learnings and breakthroughs throughout history, including the discovery of quantum computing: a cross between computation and quantum physics. In this paper, I will discuss how we can cross quantum…
After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions…
This introductory text on the basics of quantum mechanics is intended to serve as a kind of travel guide through the quantum world. It starts by asking whether quantum physics is important, or weird, or incomprehensible. It explains why…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
We describe the difficulties that advanced undergraduate and graduate students have with quantum measurement within the standard interpretation of quantum mechanics. We explore the possible origins of these difficulties by analyzing student…
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be…
Quantum Computing is an exciting field that draws from information theory, computer science, mathematics, and quantum physics to process information in fundamentally new ways. There is an ongoing race to develop practical quantum computers…
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and…