Related papers: Hilbert-space factorization is a limited and expen…
Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but…
Randomized protocols are procedures that incorporate probabilistic choices during their execution and they play a central role in quantum algorithms, spanning Hamiltonian simulation, noise mitigation, and measurement tasks. In practical…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
Gaussian processes are a powerful class of non-linear models, but have limited applicability for larger datasets due to their high computational complexity. In such cases, approximate methods are required, for example, the recently…
We propose a quantum interferometric protocol that leverages spin-dependent spatial displacements to enable high-precision parameter estimation beyond classical limits. By inducing a unitary coupling between a particles spin degree of…
We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
Recent results on the decoherent histories quantization of simple cosmological models (minisuperspace models) are described. The most important issue is the construction, from the wave function, of a probability distribution answering…
Entanglement is a key resource of quantum science for tasks that require it to be shared among participants. Within atomic, condensed matter and photonic many-body systems the distribution and sharing of entanglement is of particular…
Quantum entanglement is known as a unique quantum feature that cannot be obtained by classical physics. Over the last several decades, however, such an understanding on quantum entanglement might have confined us in a limited world of weird…
Quantum state tomography is a powerful, but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as…
In its most basic form, decision-making can be viewed as a computational process that progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally costly, meaning that the amount of uncertainty that can…
It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
The fluctuation-dissipation relation is well known for the quantum open system with energy dissipation. In this paper a similar underlying relation is found between the bath fluctuation and the dephasing of the quantum open system, of which…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…
The question is raised whether the unique decomposition of the physical Hilbert space, as emerging in the refined algebraic quantization of a constrained system, may be understood in terms of the old Klein-Gordon type quantization.
We report formulas for the joint moments of the determinantal products (det{rho})^k (det{rho^PT})^K (k=0, 1, 2,...,N; K = 0, 1, 2, 3, 4) of Hilbert-Schmidt (HS) probability distributions over the two-rebit and (K = 0, 1) two-qubit density…
We present estimators for smooth Hilbert-valued parameters, where smoothness is characterized by a pathwise differentiability condition. When the parameter space is a reproducing kernel Hilbert space, we provide a means to obtain efficient,…
Limitation of computational resources is considered as a universal principle that for simulation is as fundamental as physical laws are. It claims that all experimentally verifiable implications of physical laws can be simulated by the…