Related papers: Stronger sum uncertainty relations for non-Hermiti…
Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian conjugate) in the context of four (3 + 1)-dimensional (4D)…
We discuss some simple H\"uckel-like matrix representations of non-Hermitian operators with antiunitary symmetries that include generalized $\mathcal{PT}$ (parity transformation followed by time-reversal) symmetry. One of them exhibits…
Let $\mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson,…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds is typically complicated, and efficient procedures are known only for a handful of cases. In this paper we present procedures based…
The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…
Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem…
Heisenberg uncertainty relation is at the origin of understanding minimum uncertainty states and squeezed states of light. In the recent past, sum uncertainty relation was formulated by Maccone and Pati [Maccone and Pati, Phys. Rev. Lett.…
We introduce an elementary measure of non-commutativity between two algebras of quantum operators acting on the same Hilbert space. This quantity, which we call Mutual Averaged Non-commutativity (MAN), is a simple generalization of a type…
This paper provides a connection to the non-Hermitian operators associated with the geometric potential function $s$ and Baker-Hausdorff formula. The geometric quantum potential is considered in a precise condition. The Ri-operator as a…
In conventional Schr\"{o}dinger representation the unitarity of the evolution of bound states is guaranteed by the Hermiticity of the Hamiltonian. A non-unitary isospectral simplification of the Hamiltonian, $\mathfrak{h} \to…
In this work, we derive Robertson-Heisenberg like uncertainty relation for two incompatible observables in a pre- and post-selected (PPS) system. The newly defined standard deviation and the uncertainty relation in the PPS system have…
Universally valid uncertainty relations are proven in a model independent formulation for inherent and unavoidable extra noises in arbitrary joint measurements on single systems, from which Heisenber's original uncertainty relation is…
We show that a quantum system possessing an exact antilinear symmetry, in particular PT-symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator relating an arbitrary non-Hermitian…
Many Generalized Uncertainty Principle (GUP) models modify the inner-product measure to ensure symmetric position or momentum operators. We show that an alternate approach to these GUPs is to symmetrize the operators rather than modifying…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudo-spin observables for an arbitrary non-positive Hermitian…
Time averaging of weak values using the quantum transition path time probability distribution enables us to establish a general uncertainty principle for the weak values of two not necessarily Hermitian operators. This new principle is a…