Related papers: Frame representations of qudit quantum mechanics
We construct a representation of qudit multi-controlled unitary operators in terms of N-body angular momentum interactions. The representation is particularly convenient for odd-dimensional systems, with interesting connections to the…
All the concepts and principles necessary to understand quantum mechanics on an initial level are given in a form suitable for the non-expert. The concepts explained include visualizing the wave function, wave-particle duality, the…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared pulses. The state is represented through the Wigner function, a ``quasi-probability density'' on $\mathbb{R}^{2}$…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
A quantum mechanical observer might be describable as having a reference system that is a superposition of classical inertial reference frames. The present paper suggests a possible weighting function in such superpositions, determined by…
In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In…
Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
Discrete coherent states for a system of $n$ qubits are introduced in terms of eigenstates of the finite Fourier transform. The properties of these states are pictured in phase space by resorting to the discrete Wigner function
Quantum Implicit Neural Representations (QINRs) include components for learning and execution on gate-based quantum computers. While QINRs recently emerged as a promising new paradigm, many challenges concerning their architecture and…
In quantum circuits, qubits and the quantum gates acting on them have traditionally been analysed using matrix algebra and Dirac notation. While powerful, these can be unintuitive for conceptual understanding and rapid problem solving. In…
Finite projective geometries, especially the Fano plane, have been observed to arise in the context of certain quantum gate operators. We use Clifford algebras to explain why these geometries, both planar and higher dimensional, appear in…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
The notion of a qubit is ubiquitous in quantum information processing. In spite of the simple abstract definition of qubits as two-state quantum systems, identifying qubits in physical systems is often unexpectedly difficult. There are an…
Quantum reference frames are needed in quantum theory for much the same reasons that reference frames are in classical theories: to manifest invariance in line with fundamental relativity principles and to provide a basis for the definition…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
Symmetries are a central concept in our understanding of physics. In quantum theories, a quantum reference frame (QRF) can be used to distinguish between observables related by a symmetry. The framework of operational QRFs provides a means…
We introduce a visual representation of qubits to assist in explaining quantum computing to a broad audience. The representation follows from physical devices that we developed to explain superposition, entanglement, measurement, phases,…
We introduce an efficient method to reconstruct the Wigner function of many-mode continuous variable systems. It is based on convex optimization with semidefinite programs, and also includes a version of the maximum entropy principle, in…