Symmetry analysis of crystalline spin textures in dipolar spinor condensates

We study periodic crystalline spin textures in spinor condensates with dipolar interactions via a systematic symmetry analysis of the low-energy effective theory. By considering symmetry operations which combine real and spin space operations, we classify symmetry groups consistent with non-trivial experimental and theoretical constraints. Minimizing the energy within each symmetry class allows us to explore possible ground states.Comment: 19 pages, 4 figure

Bounds on Quantum Correlations in Bell Inequality Experiments

Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description. However, despite the importance of Bell inequalities, it is not known in general how to determine whether a given entangled state will violate a Bell inequality. This is because one can choose to make many different measurements on a quantum system to test any given Bell inequality and the optimization over measurements is a high-dimensional variational problem. In order to better understand this problem we present algorithms that provide, for a given quantum state, both a lower bound and an upper bound on the maximal expectation value of a Bell operator. Both bounds apply techniques from convex optimization and the methodology for creating upper bounds allows them to be systematically improved. In many cases these bounds determine measurements that would demonstrate violation of the Bell inequality or provide a bound that rules out the possibility of a violation. Examples are given to illustrate how these algorithms can be used to conclude definitively if some quantum states violate a given Bell inequality.Comment: 13 pages, 1 table, 2 figures. Updated version as published in PR

Better Bell Inequality Violation by Collective Measurements

The standard Bell inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that nonlocality of bipartite pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements, even without communication between the parties. For mixed states we also show that collective measurements can increase the violation of Bell inequalities, although numerical evidence suggests that the phenomenon is not common as it is for pure states.Comment: 7 pages, 4 figures and 1 table; references update

Bell inequalities for three systems and arbitrarily many measurement outcomes

We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin Bell inequality. For a small number of outcomes, we verify that our inequalities define facets of the polytope of local correlations. We investigate the quantum violations of these inequalities, in particular with respect to the Hilbert space dimension. We provide strong evidence that the maximal quantum violation can only be reached using systems with local Hilbert space dimension exceeding the number of measurement outcomes. This suggests that our inequalities can be used as multipartite dimension witnesses.Comment: v1 6 pages, 4 tables; v2 Published version with minor typos correcte

Alternative fidelity measure for quantum states

We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of "Jozsa's axioms". The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, new metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.Comment: 12 pages, 3 figures. v2 includes minor changes, new references and new numerical results (Sec. IV

Renormalization Group calculations with k|| dependent couplings in a ladder

We calculate the phase diagram of a ladder system, with a Hubbard interaction and an interchain coupling $t_\perp$. We use a Renormalization Group method, in a one loop expansion, introducing an original method to include $k_{||}$ dependence of couplings. We also classify the order parameters corresponding to ladder instabilities. We obtain different results, depending on whether we include $k_{||}$ dependence or not. When we do so, we observe a region with large antiferromagnetic fluctuations, in the vicinity of small $t_\perp$, followed by a superconducting region with a simultaneous divergence of the Spin Density Waves channel. We also investigate the effect of a non local backward interchain scattering : we observe, on one hand, the suppression of singlet superconductivity and of Spin Density Waves, and, on the other hand, the increase of Charge Density Waves and, for some values of $t_\perp$, of triplet superconductivity. Our results eventually show that $k_{||}$ is an influential variable in the Renormalization Group flow, for this kind of systems.Comment: 20 pages, 19 figures, accepted in Phys. Rev. B 71 v. 2

Neutral skyrmion configurations in the low-energy effective theory of spinor condensate ferromagnets

We study the low-energy effective theory of spinor condensate ferromagnets for the superfluid velocity and magnetization degrees of freedom. This effective theory describes the competition between spin stiffness and a long-ranged interaction between skyrmions, topological objects familiar from the theory of ordinary ferromagnets. We find exact solutions to the non-linear equations of motion describing neutral configurations of skyrmions and anti-skyrmions. These analytical solutions provide a simple physical picture for the origin of crystalline magnetic order in spinor condensate ferromagnets with dipolar interactions. We also point out the connections to effective theories for quantum Hall ferromagnets.Comment: 13 pages, 7 figure

Reexamination of a multisetting Bell inequality for qudits

The class of d-setting, d-outcome Bell inequalities proposed by Ji and collaborators [Phys. Rev. A 78, 052103] are reexamined. For every positive integer d > 2, we show that the corresponding non-trivial Bell inequality for probabilities provides the maximum classical winning probability of the Clauser-Horne-Shimony-Holt-like game with d inputs and d outputs. We also demonstrate that the general classical upper bounds given by Ji et al. are underestimated, which invalidates many of the corresponding correlation inequalities presented thereof. We remedy this problem, partially, by providing the actual classical upper bound for d less than or equal to 13 (including non-prime values of d). We further determine that for prime value d in this range, most of these probability and correlation inequalities are tight, i.e., facet-inducing for the respective classical correlation polytope. Stronger lower and upper bounds on the quantum violation of these inequalities are obtained. In particular, we prove that once the probability inequalities are given, their correlation counterparts given by Ji and co-workers are no longer relevant in terms of detecting the entanglement of a quantum state.Comment: v3: Published version (minor rewordings, typos corrected, upper bounds in Table III improved/corrected); v2: 7 pages, 1 figure, 4 tables (substantially revised with new results on the tightness of the correlation inequalities included); v1: 7.5 pages, 1 figure, 4 tables (Comments are welcome

Measurement-device-independent entanglement witnesses for all entangled quantum states

The problem of demonstrating entanglement is central to quantum information processing applications. Resorting to standard entanglement witnesses requires one to perfectly trust the implementation of the measurements to be performed on the entangled state, which may be an unjustified assumption. Inspired by the recent work of F. Buscemi [Phys. Rev. Lett. 108, 200401 (2012)], we introduce the concept of measurement-device-independent entanglement witnesses (MDI-EWs), which allow one to demonstrate entanglement of all entangled quantum states with untrusted measurement apparatuses. We show how to systematically obtain such MDI-EWs from standard entanglement witnesses. Our construction leads to MDI-EWs that are loss tolerant and can be implemented with current technology

Generating nonclassical correlations without fully aligning measurements

We investigate the scenario where spatially separated parties perform measurements in randomly chosen bases on an N-partite Greenberger-Horne-Zeilinger state. We show that without any alignment of the measurements, the observers will obtain correlations that violate a Bell inequality with a probability that rapidly approaches 1 as N increases and that this probability is robust against noise. We also prove that restricting these randomly chosen measurements to a plane perpendicular to a common direction will always generate correlations that violate some Bell inequality. Specifically, if each observer chooses their two measurements to be locally orthogonal, then the N observers will violate one of two Bell inequalities by an amount that increases exponentially with N. These results are also robust against noise and perturbations of each observer's reference direction from the common direction.Comment: v2: Essentially published version (with typos fixed, results updated in Table 2 and Figure 4 replaced); v1: 16 pages, 5 figures, 2 tables, comments welcom