Related papers: Process-theoretic characterisation of the Hermitia…
With the previous notions of bisimulation presented in literature, to check if two quantum processes are bisimilar, we have to instantiate the free quantum variables of them with arbitrary quantum states, and verify the bisimilarity of…
We study a non-Hermitian generalization of quantum systems in which an imaginary vector potential is added to the momentum operator. In the tight-binding approximation, we make the hopping energy asymmetric in the Hermitian Hamiltonian. In…
Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
We construct an abelian category C and exact functors in C which on the Grothendieck group descend to the action of a simply-laced quantum group in its adjoint representation. The braid group action in the adjoint representation lifts to an…
In this paper we continue our analysis of intertwining relations for both self-adjoint and not self-adjoint operators. In particular, in this last situation, we discuss the connection with pseudo-hermitian quantum mechanics and the role of…
In the context of the factorization method, we investigate the pseudo- Hermitian coherent states and its Hermitian counterpart coherent states under the generalized quantum condition in the framework of a position-dependent mass. By…
We carefully examine the thermodynamic consequences of the repeated partial projection model for coupling a quantum system to an arbitrary series of environments under feedback control. This paper provides observational definitions of heat…
Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…
We establish an operational theory of coherence (or of superposition) in quantum systems, by focusing on the optimal rate of performance of certain tasks. Namely, we introduce the two basic concepts - "coherence distillation" and "coherence…
We present a detailed synthetic overview of the utilisation of categorical techniques in the study of order structures together with their applications in operational quantum theory. First, after reviewing the notion of residuation and its…
The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity guarantees that the energy spectrum is real and that time evolution…
The separation of internal energy into heat and work in quantum thermodynamics is a controversial issue for a long time, and we revisit and solve this problem in this work. It is shown that the Hamiltonian plays dual roles for a quantum…
We present a description of the measurement process based on the parametric representation with environmental coherent states. This representation is specifically tailored for studying quantum systems whose environment needs being…
Discrepancies between theory and recent qBounce data have prompted renewed scrutiny of how boundary conditions are implemented for ultracold neutrons bouncing above a mirror in Earth's gravity. We apply the theory of self-adjoint extensions…
We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our…
The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
Interacting and open quantum systems can be formulated in terms of an effective non-Hermitian Hamiltonian (NHH), however, there are important constraints that must be satisfied by the effective action and the associated Green's functions.…