## Final Activity Report Summary - ENTANGLQOPT (Multipartite Entanglement in Quantum Optical Systems)

The basics of quantum mechanics have already been known for half a century, however, it has become possible only quite recently to study many-body quantum dynamics experimentally. For such an experiment one must be able to control very well the quantum system, and be able to measure its state at least at the end of the dynamics. Moreover, the quantum system must also be well isolated from the environment. The main difficulty arises since these two requirements must be fulfilled at the same time.

Several quantum optical systems offer the possibility of studying many-body quantum dynamics, such as optical lattices of bosonic two-state atoms, trapped cold ions or photonic systems obtained from parametric down-conversion. The development of the necessary technical tools were the focus of the efforts of the quantum optics community in the last decade.

One of the notions introduced relatively late in quantum theory is entanglement. The word itself is from Schrodinger, however, a modern definition is from 1989. If a two-particle system is in an entangled state then it exhibits several phenomena which could not be obtained from classical physics. Beside fundamental quantum theory, it also has connections to quantum information processing applications: entangled states can be used for quantum information processing tasks which could not be done without entanglement.

My project aimed at studying multipartite entanglement in quantum optical systems. I intended to develop methods which make it possible to study entanglement in physical systems, such as optical lattices of two-state atoms, in which full control of the system is not possible for the experimenter. That is, only collective quantities are accessible or only local measurements are possible.

In a theoretical paper, I developed methods for detecting entanglement with collective observables in the vicinity of so called Dicke states. These are quantum states which arise naturally in symmetric systems. My methods have already been used in a photonic experiment. Using my criterion was advantageous since only very few measurements were needed. Note that the large number of measurements needed for entanglement detection is a problem in many physical system.

Moreover, we developed methods for detecting various forms of multipartite entanglement (i.e. three-qubit and four-qubit entanglement) in spin chains by energy measurement. Besides, we studied other aspects of multipartite entanglement. For example, we studied the connection between non-locality and entanglement. We found a quantum state which is genuine three-qubit entangled, however, it does not violate any Bell inequality. This is surprising since genuine multiqubit entanglement is, in a sense, a strong type of entanglement thus one expects that such states must violate a Bell inequality.

Several quantum optical systems offer the possibility of studying many-body quantum dynamics, such as optical lattices of bosonic two-state atoms, trapped cold ions or photonic systems obtained from parametric down-conversion. The development of the necessary technical tools were the focus of the efforts of the quantum optics community in the last decade.

One of the notions introduced relatively late in quantum theory is entanglement. The word itself is from Schrodinger, however, a modern definition is from 1989. If a two-particle system is in an entangled state then it exhibits several phenomena which could not be obtained from classical physics. Beside fundamental quantum theory, it also has connections to quantum information processing applications: entangled states can be used for quantum information processing tasks which could not be done without entanglement.

My project aimed at studying multipartite entanglement in quantum optical systems. I intended to develop methods which make it possible to study entanglement in physical systems, such as optical lattices of two-state atoms, in which full control of the system is not possible for the experimenter. That is, only collective quantities are accessible or only local measurements are possible.

In a theoretical paper, I developed methods for detecting entanglement with collective observables in the vicinity of so called Dicke states. These are quantum states which arise naturally in symmetric systems. My methods have already been used in a photonic experiment. Using my criterion was advantageous since only very few measurements were needed. Note that the large number of measurements needed for entanglement detection is a problem in many physical system.

Moreover, we developed methods for detecting various forms of multipartite entanglement (i.e. three-qubit and four-qubit entanglement) in spin chains by energy measurement. Besides, we studied other aspects of multipartite entanglement. For example, we studied the connection between non-locality and entanglement. We found a quantum state which is genuine three-qubit entangled, however, it does not violate any Bell inequality. This is surprising since genuine multiqubit entanglement is, in a sense, a strong type of entanglement thus one expects that such states must violate a Bell inequality.