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Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or…
We investigate entanglement measures in the infinite-dimensional regime. First, we discuss the peculiarities that may occur if the Hilbert space of a bi-partite system is infinite-dimensional, most notably the fact that the set of states…
Quantum entanglement between an interfering particle and a detector for acquiring the which-path information plays a central role for enforcing Bohr's complementarity principle. However, the quantitative relation between this entanglement…
We discuss the concept of how entanglement changes with respect to different factorizations of the total algebra which describes the quantum states. Depending on the considered factorization a quantum state appears either entangled or…
Measurements in the quantum domain can exceed classical notions. This concerns fundamental questions about the nature of the measurement process itself, as well as applications, such as their function as building blocks of quantum…
We generalize a new approach to entanglement conditions for light of undefined photons numbers given in [Phys. Rev. A {\bf 95}, 042113 (2017)] for polarization correlations to a broader family of interferometric phenomena. Integrated optics…
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…
This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert…
Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a…
Entanglement is a fundamental feature of quantum mechanics, playing a crucial role in quantum information processing. However, classifying entangled states, particularly in the mixed-state regime, remains a challenging problem, especially…
Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based…
We study measures of quantum information when the space spanned by the set of accessible observables is not closed under products, i.e., we consider systems where an observer may be able to measure the expectation values of two operators,…
Entanglement and interference are both hallmark effects of quantum physics. Particularly rich dynamics arise when multiple (at least partially) indistinguishable particles are subjected to either of these phenomena. By combining both…
Entanglement plays an important role in our ability to understand, simulate, and harness quantum many-body phenomena. In this work, we investigate the entanglement spectrum for open one-dimensional systems, and propose a natural quantifier…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
We address the problem of completely characterizing multi-particle states including loss of information to unobserved degrees of freedom. In systems where non-classical interference plays a role, such as linear-optics quantum gates, such…
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
We study the genuine multipartite entanglement of arbitrary $n$-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite…
Entanglement-enhanced quantum metrology explores the utilization of quantum entanglement to enhance measurement precision. When particles in a probe are prepared into a quantum entangled state, they collectively accumulate information about…