Related papers: Defining quantumness via the Jordan product
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…
In quantum theory, the modulus-square of the inner product of two normalized Hilbert space elements is to be interpreted as the transition probability between the pure states represented by these elements. A probabilistically motivated and…
Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of…
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set $\cal A$ of operationally relevant observables. The algebraic structure of $\cal A$ selects a preferred tensor product…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
The indeterministic outcome of a measurement of an individual quantum is certified by the impossibility of the simultaneous, definite, deterministic pre-existence of all conceivable observables from physical conditions of that quantum…
We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the $\Lambda\to\infty$ limit of general relativity. This allows an…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
Quantum fields are considered as generators of infinite-dimensional Clifford algebra $Cl(\infty)$, which can be either orthogonal (in case of fermions) or symplectic (in case of bosons). A generic quantum state can be expressed as a…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
With the purpose to introduce a useful tool for researches concerning foundations of quantum mechanics and applications to quantum technologies, here we study three quantumness quantifiers for bipartite optical systems: one based on…
The existence of a real linear-space structure on the set of observables of a quantum system -- i.e., the requirement that the linear combination of two generally non-commuting observables $A,B$ is an observable as well -- is a fundamental…
In 1934, Jordan et al. gave a necessary algebraic condition, the Jordan identity, for a sensible theory of quantum mechanics. All but one of the algebras that satisfy this condition can be described by Hermitian matrices over the complexes…
The tensor product postulate of quantum mechanics states that the Hilbert space of a composite system is the tensor product of the components' Hilbert spaces. All current formalizations of quantum mechanics that do not contain this…
The Hilbert space dimension of a quantum system is the most basic quantifier of its information content. Lower bounds on the dimension can be certified in a device-independent way, based only on observed statistics. We highlight that some…
Observables of quantum or classical mechanics form algebras called quantum or classical Hamilton algebras respectively (Grgin E and Petersen A (1974) {\it J Math Phys} {\bf 15} 764\cite{grginpetersen}, Sahoo D (1977) {\it Pramana} {\bf 8}…