Related papers: Reality from maximizing overlap in the future-incl…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
I propose a new class of interpretations, {\it real world interpretations}, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one…
It is shown that, in the framework of non-relativistic quantum mechanics, any conserved Hermitian operator (which may depend explicitly on the time) is the generator of a one-parameter group of unitary symmetries of the Hamiltonian and…
A prepare-and-measure scenario is naturally described by a communication matrix that collects all conditional outcome probabilities of the scenario into a row-stochastic matrix. The set of all possible communication matrices is partially…
The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are…
In an amended version of non-Hermitian interaction picture we propose to work with the states $\psi(t)$ in a dyadic representation. The control of evolution via two conjugate Schr\"{o}diner equations then renders the usual necessity of the…
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization…
We develop a perturbative understanding of the modular Hamiltonian for a 2D CFT, divided into left and right half-spaces, with a weak local perturbation inserted in the future wedge. A formal perturbation series for the modular Hamiltonian…
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…
In the popular ${\cal PT}-$symmetry-based formulation of quantum mechanics of closed systems one can build unitary models using non-Hermitian Hamiltonians (i.e., $H \neq H^\dagger$) which are Hermitizable (so that one can write,…
Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…
Despite its common use in quantum theory, the mathematical requirement of Dirac Hermiticity of a Hamiltonian is sufficient to guarantee the reality of energy eigenvalues but not necessary. By establishing three theorems, this paper gives…
Quantum dynamics simulations of reactive molecular processes are commonly performed in a low-dimensional space spanned by highly optimized reactive coordinates. Usually, these sets of reactive coordinates consist of non-linear coordinates.…
We review the well-known Hellmann Feynman Theorem (HFT), originally developed for Hermitian systems to facilitate the calculation of forces among the molecules. Our work extends this foundational theorem to the domain of non-Hermitian…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
We in this paper study the hermiticity of Hamiltonian and energy spectrum for the SU(1; 1) systems. The Hermitian Hamiltonian can possess imaginary eigenvalues in contrast with the common belief that hermiticity is a suffcient condition for…
Observable operator models (OOMs) offer a powerful framework for modelling stochastic processes, surpassing the traditional hidden Markov models (HMMs) in generality and efficiency. However, using OOMs to model infinite-dimensional…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
Several proposals to deal with the dynamics of general relativity involve gauge fixings or the introduction matter fields in terms of which the theory is deparameterized. The resulting theories have true Hamiltonians for their evolution…
We propose a modification of a recently introduced generalized translation operator, by including a $q$-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator $\hat{p}_q$, and its canonically…