We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in "artificial" magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.

In spite of many results in quantum information theory, the complex nature of compound systems is far from being clear. In general the information is a mixture of local, and non-local ("quantum") information. It is important from both pragmatic and theoretical points of view to know relationships between the two components. To make this point more clear, we develop and investigate the quantum information processing paradigm in which parties sharing a multipartite state distill local information. The amount of information which is lost because the parties must use a classical communication channel is the deficit. This scheme can be viewed as complementary to the notion of distilling entanglement. After reviewing the paradigm in detail, we show that the upper bound for the deficit is given by the relative entropy distance to so-called pseudo-classically correlated states; the lower bound is the relative entropy of entanglement. This implies, in particular, that any entangled state is informationally nonlocal i.e. has nonzero deficit. We also apply the paradigm to defining the thermodynamical cost of erasing entanglement. We show the cost is bounded from below by relative entropy of entanglement. We demonstrate the existence of several other non-local phenomena which can be found using the paradigm of local information. For example, we prove the existence of a form of non-locality without entanglement and with distinguishability. We analyze the deficit for several classes of multipartite pure states and obtain that in contrast to the GHZ state, the Aharonov state is extremely nonlocal (and in fact can be thought of as quasi-nonlocalisable). We also show that there do not exist states, for which the deficit is strictly equal to the whole informational content (bound local information). We discuss the relation of the paradigm with measures of classical correlations introduced earlier. It is also proven that in the one-way scenario, the deficit is additive for Bell diagonal states. We then discuss complementary features of information in distributed quantum systems. Finally we discuss the physical and theoretical meaning of the results and pose many open questions. Contents

A new paradigm for distributed quantum systems where information is a valuable resource is developed. After finding a unique measure for information, we construct a scheme for it's manipulation in analogy with entanglement theory. In this scheme instead of maximally entangled states, two parties distill local states. We show that, surprisingly, the main tools of entanglement theory are general enough to work in this opposite scheme. Up to plausible assumptions, we show that the amount of information that must be lost during the protocol of concentration of local information can be expressed as the relative entropy distance from some special set of states.The notion of quantum correlations is a more general than entanglement [1,2]. A formal measure of quantum correlations in measurements (quantum discord) [2] was found, based primarily on an entropy-like function. Recently, the first operational approach to quantify quantum correlations was introduced in [3]. Subsequently, a similar approach was used to justify a physical interpretation of (the optimized) quantum discord [4]. The results of [3] was based on the idea that using a system in a pure state one can draw work from a single heat bath. This scenario was used in the case of distributed quantum systems: Alice and Bob share a state, have local heat baths, and can use only local operations and classical communication (LOCC), to concentrate the information contained in the state, in order to draw work. The amount of work drawn by LOCC is usually smaller than the one extractable if Alice and Bob can use global operations. The resulting difference denoted by the deficit ∆ accounts for the part of correlations that must be lost during classical communication, thus describing purely quantum correlations. In the case of ∆ for pure states, it was argued to be exactly equal to the entanglement while for mixed states it is supposed to be an independent quantity. In this context, it is clear that understanding the problem of concentration of information will provide valuable insight into the nature of quantum correlations. Yet the early development of these ideas [3,5] indicated that the proposed scenario is completely different that anything we had in quantum information theory so far. In particular the serious difficulty (which shall be removed in this paper) was that one is not even able to obtain (without additional assumptions) the value of ∆ in the simplest case of a two-qubit Bell state.In this context basic questions arise: (i) What is the connection between the above thermodynamical quantification of quantum correlations and the main concepts of quantum information theory? (ii) Can we formulate the concentration of information within a framework of manipulating resources like in entanglement theory? An even more basic question is: (iii) can we give up thermodynamics, and formulate the problem solely in terms of quantum information? To see the importance of the latter, let us note that the discovery of teleportation and Shor's algorithm was possible by restrict...

More than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication (LOCC) are allowed. We show that four Bell states cannot be discriminated by LOCC, even probabilistically, using the separability properties of a four-party unlockable bound entangled state. Using an existing inequality among the measures of entanglement, we show that any three Bell states cannot be discriminated with certainty by LOCC. Exploiting the inequality, we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed states.