All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory} But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding However, it appeared that this new resource is
very complex and difficult to detect Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon A basic role of entanglement
witnesses in detection of entanglement is emphasized

Quantum entanglement

http://cds.cern.ch/record/262851/files/9405029.pdf

Supersymmetry and quantum mechanics

Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance

We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation and generating functions of all classes of orthogonal polynomials in this scheme. In chapeter 2 we give all limit relation between different classes of orthogonal polynomials listed in the Askey-scheme. 
In chapter 3 we list the q-analogues of the polynomials in the Askey-scheme. We give their definition, orthogonality relation, three term recurrence relation and generating functions. In chapter 4 we give the limit relations between those basic hypergeometric orthogonal polynomials. Finally in chapter 5 we point out how the `classical` hypergeometric orthogonal polynomials of the Askey-scheme can be obtained from their q-analogues.

/pdf/the-askey-scheme-of-hypergeometric-orthogonal-polynomials-46afheftah.pdf

The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

The coherent superposition of states, in combination with the quantization of observables, represents one of the most fundamental features that mark the departure of quantum mechanics from the classical realm. Quantum coherence in many-body systems embodies the essence of entanglement and is an essential ingredient for a plethora of physical phenomena in quantum optics, quantum information, solid state physics, and nanoscale thermodynamics. In recent years, research on the presence and functional role of quantum coherence in biological systems has also attracted a considerable interest. Despite the fundamental importance of quantum coherence, the development of a rigorous theory of quantum coherence as a physical resource has only been initiated recently. In this Colloquium we discuss and review the development of this rapidly growing research field that encompasses the characterization, quantification, manipulation, dynamical evolution, and operational application of quantum coherence.

/pdf/colloquium-quantum-coherence-as-a-resource-qzhyp2vogb.pdf

Colloquium: quantum coherence as a resource

Quantum-enhanced measurements exploit quantum mechanical effects for increasing the sensitivity of measurements of certain physical parameters and have great potential for both fundamental science and concrete applications. Most of the research has so far focused on using highly entangled states, which are, however, difficult to produce and to stabilize for a large number of constituents. In the following we review alternative mechanisms, notably the use of more general quantum correlations such as quantum discord, identical particles, or non-trivial hamiltonians; the estimation of thermodynamical parameters or parameters characterizing non-equilibrium states; and the use of quantum phase transitions. We describe both theoretically achievable enhancements and enhanced sensitivities, not primarily based on entanglement, that have already been demonstrated experimentally, and indicate some possible future research directions.

/pdf/quantum-enhanced-measurements-without-entanglement-4lg6wtlzh1.pdf

Quantum-enhanced measurements without entanglement

We show that two, noninteracting two-level systems, immersed in a common bath, can become mutually entangled when evolving according to a Markovian, completely positive reduced dynamics.

https://arxiv.org/pdf/quant-ph/0307052.pdf

Environment induced entanglement in Markovian dissipative dynamics.

Quantum Theory of Irreversibility: Open Systems and Continuum Mechanics.- Selected Aspects of Markovian and Non-Markovian Quantum Master Equations.- Aspects of Open Quantum Dynamics.- Concepts and Methods in the Theory of Open Quantum Systems.- Decoherence-Free Subspaces and Subsystems.- Controlled Quantum Open Systems.- Three Different Manifestations of the Quantum Zeno Effect.- Progressive Decoherence and Total Environmental Disentanglement.- Dynamics of Dissipative Quantum Systems: From Path Integrals to Master Equations.- Quantum Entropies in a Classical Context.- Irreversibility and the Foundations of Quantum Mechanics.- An Attempt at Relativistic Spontaneous Localization Theory.- The Quantum Jump Approach and Quantum Trajectories.- Irreversibility, Resonances and Rigged Hilbert Spaces.- Markovian Master Equations and Resonances in Quantum Open Systems.- A New Topology for an Axoim of Quantum Mechanics.- The Importance of Boundary Conditions in Quantum Mechanics.- Time Asymmetric Quantum Mechanics and Relativistic Resonances.- Irreversibility in the Framework of Hermitian and Non-Hermitian Treatments of Resonance States.

Irreversible Quantum Dynamics

We review the standard treatment of open quantum systems in relation to quantum entanglement, analyzing, in particular, the behavior of bipartite systems immersed in the same environment. We first focus upon the notion of complete positivity, a physically motivated algebraic constraint on the quantum dynamics, in relation to quantum entanglement, i.e. the existence of statistical correlations which can not be accounted for by classical probability. We then study the entanglement power of heat baths versus their decohering properties, a topic of increasing importance in the framework of the fast developing fields of quantum information, communication and computation. The presentation is self contained and, through several examples, it offers a detailed survey of the physics and of the most relevant and used techniques relative to both quantum open system dynamics and quantum entanglement.

Open quantum dynamics: complete positivity and entanglement

The master equation describing the completely positive time evolution of a uniformly accelerated two-level system in weak interaction with a scalar field in the Minkowski vacuum is derived and explicitly solved. The moving system is found to be subjected to dissipation that drives its density matrix to a purely thermal equilibrium state, exhibiting a nonvanishing probability of spontaneous excitation, this phenomenon being usually referred to as the Unruh effect. Remarkably, when the uniformly accelerating system is composed by two, independent two-level atoms, the corresponding asymptotic, equilibrium state turns out to be entangled.

Roberto Floreanini

Papers

Quantum-enhanced measurements without entanglement

Environment induced entanglement in Markovian dissipative dynamics.

Irreversible Quantum Dynamics

Open quantum dynamics: complete positivity and entanglement

Entanglement generation in uniformly accelerating atoms: Reexamination of the Unruh effect