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We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
We present a second quantization description of frequency-based continuous variables quantum computation in the subspace of single photons. For this, we define frequency and time operators using the free field Hamiltonian and its Fourier…
Dynamical systems can be analyzed via their Frobenius-Perron transfer operator and its estimation from data is an active field of research. Recently entropic transfer operators have been introduced to estimate the operator of deterministic…
While in relativity theory space evolves over time into a single entity known as spacetime, quantum theory lacks a standard notion of how to encapsulate the dynamical evolution of a quantum state into a single "state over time". Recently it…
Quantum trajectories and superoperator algorithms implemented within the matrix product state (MPS) framework are powerful tools to simulate the real-time dynamics of open dissipative quantum systems. As for the unitary case, the reachable…
The notion of operator growth in quantum systems furnishes a bridge between transport and the generation of entanglement between different parts of the system under quantum dynamics. We define a measure of operator growth in terms of…
Hamiltonian Mechanics works for conserved systems and Quantum Mechanics is given in Hamiltonian language. It is considered that complexifying the quantum Hamiltonian, a balanced loss and gain model can be created. The usual mathematics of…
The standard toolkit of operators to probe quanta of geometry in loop quantum gravity consists in area and volume operators as well as holonomy operators. New operators have been defined, in the U(N) framework for intertwiners, which allow…
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect,…
We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation regardless of its initial condition and the path of its evolution in the state space, and we…
We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we…
By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators (which considers normal ordered, antinormally ordered and Weyl…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
How to introduce thermodynamics to quantum mechanics ? Among from numerous possibilities of solving this task, the simple choice is here: The conventional von Neumann equation deals with a density operator whose probability weights are time…
We derive an expression for a density operator estimated via Bayesian quantum inference in the limit of an infinite number of measurements. This expression is derived under the assumption that the reconstructed system is in a pure state. In…
We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions.…
Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators…