Measures of entanglement in multipartite bound entangled states

Bound entangled states are states that are entangled but from which no entanglement can be distilled if all parties are allowed only local operations and classical communication. However, in creating these states one needs nonzero entanglement resources to start with. Here, the entanglement of two distinct multipartite bound entangled states is determined analytically in terms of a geometric measure of entanglement and a related quantity. The results are compared with those for the negativity and the relative entropy of entanglement.Comment: 5 pages, no figure; title change

From Bell's Theorem to Secure Quantum Key Distribution

Any Quantum Key Distribution (QKD) protocol consists first of sequences of measurements that produce some correlation between classical data. We show that these correlation data must violate some Bell inequality in order to contain distillable secrecy, if not they could be produced by quantum measurements performed on a separable state of larger dimension. We introduce a new QKD protocol and prove its security against any individual attack by an adversary only limited by the no-signaling condition.Comment: 5 pages, 2 figures, REVTEX

Multipartite unlockable bound entanglement in the stabilizer formalism

We find an interesting relationship between multipartite bound entangled states and the stabilizer formalism. We prove that if a set of commuting operators from the generalized Pauli group on $n$ qudits satisfy certain constraints, then the maximally mixed state over the subspace stabilized by them is an unlockable bound entangled state. Moreover, the properties of this state, such as symmetry under permutations of parties, undistillability and unlockability, can be easily explained from the stabilizer formalism without tedious calculation. In particular, the four-qubit Smolin state and its recent generalization to even number of qubits can be viewed as special examples of our results. Finally, we extend our results to arbitrary multipartite systems in which the dimensions of all parties may be different.Comment: 7 pages, no figur

Relative entropy of entanglement for certain multipartite mixed states

We prove conjectures on the relative entropy of entanglement (REE) for two families of multipartite qubit states. Thus, analytic expressions of REE for these families of states can be given. The first family of states are composed of mixture of some permutation-invariant multi-qubit states. The results generalized to multi-qudit states are also shown to hold. The second family of states contain D\"ur's bound entangled states. Along the way, we have discussed the relation of REE to two other measures: robustness of entanglement and geometric measure of entanglement, slightly extending previous results.Comment: Single column, 22 pages, 9 figures, comments welcom

Nonlocality in many-body quantum systems detected with two-body correlators

Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Science 344, 1256 (2014)]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states---ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.Comment: 46 pages (25.2 + appendices), 7 figure

Key distillation from quantum channels using two-way communication protocols

We provide a general formalism to characterize the cryptographic properties of quantum channels in the realistic scenario where the two honest parties employ prepare and measure protocols and the known two-way communication reconciliation techniques. We obtain a necessary and sufficient condition to distill a secret key using this type of schemes for Pauli qubit channels and generalized Pauli channels in higher dimension. Our results can be applied to standard protocols such as BB84 or six-state, giving a critical error rate of 20% and 27.6%, respectively. We explore several possibilities to enlarge these bounds, without any improvement. These results suggest that there may exist weakly entangling channels useless for key distribution using prepare and measure schemes.Comment: 21 page

Optimal distillation of a GHZ state

We present the optimal local protocol to distill a Greenberger-Horne-Zeilinger (GHZ) state from a single copy of any pure state of three qubits.Comment: RevTex, 4 pages, 2 figures. Published version, some references adde

A classification of entanglement in three-qubit systems

We present a classification of three-qubit states based in their three-qubit and reduced two-qubit entanglements. For pure states these criteria can be easily implemented, and the different types can be related with sets of equivalence classes under Local Unitary operations. For mixed states characterization of full tripartite entanglement is not yet solved in general; some partial results will be presented here.Comment: Shortened version. Accepted in EPJ

Control químico de las malezas en ajíes dulces

Two herbicide experiments with sweet cherry peppers were conducted in a Fraternidad clay at Lajas Substation from 1989 to 1990. In the first experiment, clomazone at 1.68 and 3.36 kg ai/ha applied pre-plant and incorporated, as well as fluazifop at 0.42 and 0.84 applied postemergence, gave excellent control of most grasses. Oxyfluorfen at 0.20 kg ai/ha as a pre-plant followed by bentazon at 1.12 kg ai/ha and fluazifop at 0.42 kg ai/ha also provided excellent weed control. The highest sweet cherry pepper yield was obtained with the hand-weeded control. It was then followed by oxyfluorfen at 0,20 kg ai/ha, then followed by bentazon + fluazifop mixture. The treatment with fluazifop at 0.42 kg ai/ha as a postemergence + one supplementary handweeding ranked third in yield. The above treatments did not differ significantly in yield. In the second experiment, colmazone at 2.24 kg ai/ha as a pre-plant, followed by three post directed application of paraquat at 0.56 kg ai/ha, gave the best weed control. Oxyfluorfen at 0.56 kg ai/ha as a pre-plant followed by bentazon at 1.12 kg ai/ha and fluazifop at 0.42 kg ai/ha mixture, also gave excellent weed control. The highest cherry pepper yield was obtained with clomazone at 2.24 kg ai/ha plus three applications of paraquat at 0.56kg ai/ha. This yield was followed by that with oxyfluorfen at 0.56 kg ai/ha followed by bentazone and fluazifop mixture. Napropamide at 2.24 kg ai/ha as a pre-plant, followed by three post directed applications of paraquat at 0.56 kg ai/ha, was ranked third. A good yield was also obtained with Napropamide at 2.24 kg ai/ha as a pre-plant followed by bentazon at 2.24 kg ai/ha and fluazifop at 0.42 kg ai/ha mixture. Yields did not differ significantly with these treatments.En un suelo Fraternidad de la Substación Experimental Agrícola de Lajas se realizaron dos experimentos con herbicidas en ají dulce de 1989 a 1990. En el primer experimento se encontró que clomazone a razón de 1.68 y 3.36 kg. p.a./ha. aplicado presiembra e incorporado como el fluazifop-P a razón de 0.42 y 0.84 kg. p.a./ha. como posemergente reprimieron las gramíneas eficazmente hasta 6 semanas después del trasplante. El oxyfiuorfen a razón de 0.20 kg. p.a./ha. como presiembra seguido por la mezcla bentazon a 1.12 kg. p.a./ha. proveyó un control excelente de la mayoría de las malezas. El rendimiento más alto de ajíes se obtuvo con el desyerbo a mano. A este rendimiento le seguió el del tratamiento de oxifluorfen a razón de 0.20 kg. p.a./ha. como presiembra + la mezcla de bentazon a 1.12 kg. p.a./ha. y fluazifop-P a 0.42 kg. p.a./ha. como posemergente. El fluazifop-P a razón de 0.42 kg. p.a./ha. + un desyerbo suplementario a mano fue tercero en rendimiento. No hubo diferencias estadísticamente significativas (0.05) de probabilidad con estos tres tratamientos. En el segundo experimento, clomazone a razón de 2.24 kg. p.a./ha. como presiembra seguido por el paraquat a razón de 0.56 kg. p.a./ha. (tres veces dirigidos) controló excelentemente la mayoría de las malezas. Oxifluorfen a razón de 0.56 kg. p.a./ha. como presiembra seguido por la mezcla de bentazon a 2.24 kg. p.a./ha. y fluazifop-P a 0.42 kg. p.a./ha. como posemergente controló eficientemente. El rendimiento más alto se obtuvo con el clomazone a razón de 2.24 kg. p.a./ha. como presiembra seguido por la aplicación dirigida de paraquat a razón de 0.56 kg p.a./ha. A este rendimiento le siguió el de oxifluorfen a razón de 0.56 kg. p.a./ha. Napropamide a razón de 2.24 kg. p.a./ha. seguido por paraquat a 0.56 kg. p.a./ha. ocupó el tercer lugar. Napropamide a razón de 2.24 kg. p.a./ha. seguido por la mezcla de bentazon a 2.24 kg. p.a./ha. y fluazifop-P a 0.42 kg. p.a./ha. obtuvo el cuarto lugar. En estos cuatro tratamientos no hubo diferencias significativas (P = 0.05) en rendimiento

Perfect Quantum Privacy Implies Nonlocality

Private states are those quantum states from which a perfectly secure cryptographic key can be extracted. They represent the basic unit of quantum privacy. In this work we show that all states belonging to this class violate a Bell inequality. This result establishes a connection between perfect privacy and nonlocality in the quantum domain.Comment: 4 pages, published versio