相关论文: On positive maps, entanglement and quantization

We study random unconditional convergence for a basis in a Banach space. The connections between this notion and classical unconditionality are explored. In particular, we analyze duality relations, reflexivity, uniqueness of these bases…

We study the effects of entanglement and control parameters on the energy landscape and optimization performance of the variational quantum circuit. Through a systematic analysis of the Hessian spectrum, we characterize the local geometry…

We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…

In this manuscript, we present a general and exact method for classicalizing the dynamics of any $N$-level quantum system, transforming quantum evolution into a classical-like framework using the geometry of complex projective spaces…

The real plane with its set of orientations or angles in $[0,\pi)$ is the simplest non trivial example of a (projective) Hilbert space and provides nice illustrations of quantum formalism. We present some of them, namely covariant integral…

We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…

The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…

A linearized variant of relative entropy is used to quantify in a unified scheme the different kinds of correlations in a bipartite quantum system. As illustration, we consider a two-qubit state with parity and exchange symmetries for which…

Quantum entanglement in 3 spatial dimensions is studied in systems with physical boundaries when an entangling surface intersects the boundary. We show that there are universal logarithmic boundary terms in the entanglement R\'{e}nyi…

This paper proposes an approach of the unified consideration of classical and quantum mechanics from the standpoint of the complex analysis effects. It turns out that quantization can be interpreted in terms of the Riemann surface…

Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…

Quantum information processing protocols are efficiently implemented on spin-$\frac{1}{2}$ networks. A quantum communication protocol generally involves a certain number of parties having local access to a subset of a larger system, whose…

Quantum correlations represent a fundamental tool for studies ranging from basic science to quantum technologies. Different non-classical correlations have been identified and studied, as entanglement and discord. In this Paper we explore…

Quantum entanglement is at the heart of many tasks in quantum information. Apart from simple cases (low dimensions, few particles, pure states), however, the mathematical structure of entanglement is not yet fully understood. This tutorial…

Quantum information is about the entanglement of states. To this starting point we add parameters whereby a single state becomes a non-vanishing section of a bundle. We consider through examples the possible entanglement patterns of…

Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…

This note shows how quantum entanglement may be simulated in classical computing. The simulated entanglement protocol is implemented using oblivious transfer in the simplest case and other many-to-one mappings in more general cases. For the…

The problem of conditions on the initial correlations between the system and the environment that lead to completely positive (CP) or not-completely positive (NCP) maps has been studied by various authors. Two lines of study may be…

We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…

We formulate the classical polarization theory for light by using entanglement analysis. We demonstrate a route to a systematic and consistent measure of ordinary light polarization that extends automatically to a new understanding of the…