Related papers: Wigner's Theorem for stabilizer states and quantum…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
We consider the classical minisuperspace model describing a closed, homogeneous and isotropic Universe, with a positive cosmological constant. Upon canonical quantization, the infinite number of possible operator orderings in the quantum…
For families of Hamiltonians defined by parts that are local, the most general definition of a symmetry algebra is the commutant algebra, i.e., the algebra of operators that commute with each local part. Thinking about symmetry algebras as…
There exist many attempts to define a Wigner function for qudits, each of them coming with its advantages and limitations. The existing finite versions have simple definitions, but they are artificial in their construction and do not allow…
We analyze and further develop a new method to represent the quantum state of a system of $n$ qubits in a phase space grid of $N\times N$ points (where $N=2^n$). The method, which was recently proposed by Wootters and co--workers (Gibbons…
Schur-Weyl duality is a ubiquitous tool in quantum information. At its heart is the statement that the space of operators that commute with the tensor powers of all unitaries is spanned by the permutations of the tensor factors. In this…
I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
Using simple algebraic methods along with an analogy to the BFSS model, we explore the possible (target) spacetime symmetries that may appear in a matrix description of de Sitter gravity. Such symmetry groups could arise in two ways, one…
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras. Subject to some reasonable constraints, we show that no such composite exists having the exceptional Jordan algebra as a direct…
The symmetry algebra of the N-dimensional anisotropic quantum harmonic oscillator with rational ratios of frequencies is constructed by a method of general applicability to quantum superintegrable systems. The special case of the 3-dim…
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$ associated with a…
Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the…
A new definition of the Wigner function for quantum fields coupled to curved space--time and an external Yang--Mills field is studied on the example of a scalar and a Dirac fields. The definition uses the formalism of the tangent bundles…
In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the…
An n-particle 3-dimensional Wigner quantum oscillator model is constructed explicitly. It is non-canonical in that the usual coordinate and linear momentum commutation relations are abandoned in favour of Wigner's suggestion that Hamilton's…
It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understanding of the probabilistic or information theoretic foundations…
The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered…