相关论文: A probabilistic operator symbol framework for quan…

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…

We investigate the following generalisation of the entropy of quantum measurement. Let H be an infinite-dimensional separable Hilbert space with a 'density' operator {\rho}, tr {\rho}=1. Let I(P)\in R be defined for any partition P =…

Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run…

For one qubit systems, we present a short, elementary argument characterizing unital quantum operators in terms of their action on Bloch vectors. We then show how our approach generalizes to multi-qubit systems, obtaining inequalities that…

Quantum state tomography is the standard technique for reconstructing a quantum state from experimental data. In the regime of finite statistics, experimental data cannot give perfect information about the quantum state. A common way to…

We present a brief review of discrete structures in a finite Hilbert space, relevant for the theory of quantum information. Unitary operator bases, mutually unbiased bases, Clifford group and stabilizer states, discrete Wigner function,…

We introduce a general mapping for encoding quantum communication protocols involving pure states of multiple qubits, unitary transformations, and projective measurements into another set of protocols that employ coherent states of light in…

We develop a technique for single qubit quantum state tomography using the mathematical setup of generalized quantization scheme for games. In our technique Alice sends an unknown pure quantum state to Bob who appends it with |0><0| and…

Matrix representations of quantum operators are computationally complete but often obscure the structural topology of information flow within a quantum circuit \cite{nielsen2000}. In this paper, we introduce a generalized graph-theoretic…

A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose…

Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or…

The concept of directionally unbiased optical multiports is introduced, in which photons may reflect back out the input direction. A linear-optical implementation is described, and the simplest three-port version studied. Symmetry arguments…

Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical…

Quantum tomography is an important tool for obtaining information about the quantum state from experimental data. In this study, we conduct a comparative analysis of various quantum tomography protocols, including protocols based on highly…

The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…

Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…

We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…

We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous…

We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a…

We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…