Package of facts and theorems for efficiently generating entanglement criteria for many qubits

We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states. These bonds are found from the properties of commutativity graphs of operators used in the criterion. We present two examples of criteria constructed according to our method. One of them detects genuine 5-qubit entanglement without ever referring to correlations between all five qubits.Comment: 5 pages, 4 figure

N-particle nonclassicality without N-particle correlations

Most of known multipartite Bell inequalities involve correlation functions for all subsystems. They are useless for entangled states without such correlations. We give a method of derivation of families of Bell inequalities for N parties, which involve, e.g., only (N-1)-partite correlations, but still are able to detect proper N-partite entanglement. We present an inequality which reveals five-partite entanglement despite only four-partite correlations. Classes of inequalities introduced here can be put into a handy form of a single non-linear inequality. An example is given of an N qubit state, which strongly violates such an inequality, despite having no N-qubit correlations. This surprising property might be of potential value for quantum information tasks.Comment: 5 page

Rotational invariance as an additional constraint on local realism

Rotational invariance of physical laws is a generally accepted principle. We show that it leads to an additional external constraint on local realistic models of physical phenomena involving measurements of multiparticle spin 1/2 correlations. This new constraint rules out such models even in some situations in which standard Bell inequalities allow for explicit construction of such models. The whole analysis is performed without any additional assumptions on the form of local realistic models.Comment: 4 page

Interference contrast in multi-source few photon optics

Many recent experiments employ several parametric down conversion (PDC) sources to get multiphoton interference. Such interference has applications in quantum information. We study here how effects due to photon statistics, misalignment, and partial distinguishability of the PDC pairs originating from different sources may lower the interference contrast in the multiphoton experiments.Comment: 23 pages, 9 figures, journal versio

Magnetic Susceptibility as a Macrosopic Entaglement Witness

We show that magnetic susceptibility can reveal spin entanglement between individual constituents of a solid, while magnetisation describes their local properties. We then show that these two thermodynamical quantities satisfy complementary relation in the quantum-mechanical sense. It describes sharing of (quantum) information in the solid between spin entanglement and local properties of its individual constituents. Magnetic susceptibility is shown to be a macroscopic spin entanglement witness that can be applied without complete knowledge of the specific model (Hamiltonian) of the solid.Comment: 6 Pages, 2 figures, revtex

Do all pure entangled states violate Bell's inequalities for correlation functions?

Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisin's theorem). We show that there exist pure entangled N>2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description.Comment: 4 pages, journal versio

Family of Zeilinger-Horne-Greenberger "W" states lead to stronger nonclassicality than family of Greenberger-Horne-Zeilinger "GHZ" states

The N-qubit states of the W class, for N>10, lead to more robust (against noise admixture) violations of local realism, than the GHZ states. These violations are most pronounced for correlations for a pair of qubits, conditioned on specific measurement results for the remaining (N-2) qubits. The considerations provide us with a qualitative difference between the W state and GHZ state in the situation when they are separately sent via depolarizing channels. For sufficiently high amount of noise in the depolarizing channel, the GHZ states cannot produce a distillable state between two qubits, whereas the W states can still produce a distillable state in a similar situation.Comment: v3: 7 pages, 2 figures, REVTeX4; v2: result on comparative yield of singlets added, 1 new figur

Quantum physics meets biology

Quantum physics and biology have long been regarded as unrelated disciplines, describing nature at the inanimate microlevel on the one hand and living species on the other hand. Over the last decades the life sciences have succeeded in providing ever more and refined explanations of macroscopic phenomena that were based on an improved understanding of molecular structures and mechanisms. Simultaneously, quantum physics, originally rooted in a world view of quantum coherences, entanglement and other non-classical effects, has been heading towards systems of increasing complexity. The present perspective article shall serve as a pedestrian guide to the growing interconnections between the two fields. We recapitulate the generic and sometimes unintuitive characteristics of quantum physics and point to a number of applications in the life sciences. We discuss our criteria for a future quantum biology, its current status, recent experimental progress and also the restrictions that nature imposes on bold extrapolations of quantum theory to macroscopic phenomena.Comment: 26 pages, 4 figures, Perspective article for the HFSP Journa

Quantum Impurity Entanglement

Entanglement in J_1-J_2, S=1/2 quantum spin chains with an impurity is studied using analytic methods as well as large scale numerical density matrix renormalization group methods. The entanglement is investigated in terms of the von Neumann entropy, S=-Tr rho_A log rho_A, for a sub-system A of size r of the chain. The impurity contribution to the uniform part of the entanglement entropy, S_{imp}, is defined and analyzed in detail in both the gapless, J_2 <= J_2^c, as well as the dimerized phase, J_2>J_2^c, of the model. This quantum impurity model is in the universality class of the single channel Kondo model and it is shown that in a quite universal way the presence of the impurity in the gapless phase, J_2 <= J_2^c, gives rise to a large length scale, xi_K, associated with the screening of the impurity, the size of the Kondo screening cloud. The universality of Kondo physics then implies scaling of the form S_{imp}(r/xi_K,r/R) for a system of size R. Numerical results are presented clearly demonstrating this scaling. At the critical point, J_2^c, an analytic Fermi liquid picture is developed and analytic results are obtained both at T=0 and T>0. In the dimerized phase an appealing picure of the entanglement is developed in terms of a thin soliton (TS) ansatz and the notions of impurity valence bonds (IVB) and single particle entanglement (SPE) are introduced. The TS-ansatz permits a variational calculation of the complete entanglement in the dimerized phase that appears to be exact in the thermodynamic limit at the Majumdar-Ghosh point, J_2=J_1/2, and surprisingly precise even close to the critical point J_2^c. In appendices the relation between the finite temperature entanglement entropy, S(T), and the thermal entropy, S_{th}(T), is discussed and and calculated at the MG-point using the TS-ansatz.Comment: 62 pages, 27 figures, JSTAT macro