Related papers: Hilbert space-valued Gaussian processes, and quant…
We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
This paper introduces the Quantum Covariance Embedding, which embeds Positive Operator-Valued Measures into a tensor product of a Reproducing Kernel Hilbert Space and the quantum state space via a tensorized Bochner integral. This…
This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a…
The characterization of a unitary gate is experimentally accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to reconstruct the underlying operator. The process matrix is typically…
We describe quantization designs which lead to asymptotically and order optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a crucial role to achieve these rates. For the development of a…
Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
The expectation value <O> of an arbitrary operator O can be obtained via a universal measuring apparatus that is independent of O, by changing only the data-processing of the outcomes. Such a ``universal detector'' performs a joint…
We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum…
In a previous article we have introduced an operator representing the three-dimensional scalar curvature in loop quantum gravity. In this article we examine the new curvature operator in the setting of quantum-reduced loop gravity. We…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
Various approaches of defining and determining work performed on a quantum system are compared. Any operational definition of work, however, must allow for two facts, first, that work characterizes a process rather than an instantaneous…
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information…
By taking the need for quantum reference frames into account, it is shown that Hilbert-space factorization is a dissipative process requiring on the order of kT to reduce by one bit an observer's uncertainty in the provenance of a…
We derive a precise link between series expansions of Gaussian random vectors in a Banach space and Parseval frames in their reproducing kernel Hilbert space. The results are applied to pathwise continuous Gaussian processes and a new…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
Inspired by some problems in Quantum Information Theory, we present some results concerning decompositions of positive operators acting on finite dimensional Hilbert spaces. We focus on decompositions by families having geometrical symmetry…
This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely…
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…