Nonlinear Quantum Mechanics at the Planck Scale

I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear effects can be of comparable magnitude to the linear ones and still be highly suppressed at low energies. This can offer alternative approaches to quantum gravity and to the evolution of the early universe.Comment: Talk given at the International Quantum Structures 2004 meeting, 16 pages LaTe

Quadratic Bell inequalities as tests for multipartite entanglement

This letter presents quantum mechanical inequalities which distinguish, for systems of $N$ spin-\half particles ($N>2$), between fully entangled states and states in which at most $N-1$ particles are entangled. These inequalities are stronger than those obtained by Gisin and Bechmann-Pasquinucci [Phys.\ Lett. A {\bf 246}, 1 (1998)] and by Seevinck and Svetlichny [quant-ph/0201046].Comment: 4 pages, including 1 figure. Typo's removed and one proof simplified in revised versio

The no-signaling condition and quantum dynamics

We show that the basic dynamical rules of quantum physics can be derived from its static properties and the condition that superluminal communication is forbidden. More precisely, the fact that the dynamics has to be described by linear completely positive maps on density matrices is derived from the following assumptions: (1) physical states are described by rays in a Hilbert space, (2) probabilities for measurement outcomes at any given time are calculated according to the usual trace rule, (3) superluminal communication is excluded. This result also constrains possible non-linear modifications of quantum physics.Comment: 4 page

Quantum networks reveal quantum nonlocality

The results of local measurements on some composite quantum systems cannot be reproduced classically. This impossibility, known as quantum nonlocality, represents a milestone in the foundations of quantum theory. Quantum nonlocality is also a valuable resource for information processing tasks, e.g. quantum communication, quantum key distribution, quantum state estimation, or randomness extraction. Still, deciding if a quantum state is nonlocal remains a challenging problem. Here we introduce a novel approach to this question: we study the nonlocal properties of quantum states when distributed and measured in networks. Using our framework, we show how any one-way entanglement distillable state leads to nonlocal correlations. Then, we prove that nonlocality is a non-additive resource, which can be activated. There exist states, local at the single-copy level, that become nonlocal when taking several copies of it. Our results imply that the nonlocality of quantum states strongly depends on the measurement context.Comment: 4 + 3 pages, 4 figure

Approximate quantum cloning and the impossibility of superluminal information transfer

We show that nonlocality of quantum mechanics cannot lead to superluminal transmission of information, even if most general local operations are allowed, as long as they are linear and trace preserving. In particular, any quantum mechanical approximate cloning transformation does not allow signalling. On the other hand, the no-signalling constraint on its own is not sufficient to prevent a transformation from surpassing the known cloning bounds. We illustrate these concepts on the basis of some examples.Comment: 4 pages, 1eps figur

Trophic Relationships and Food Supply of Heterotrophic Animals in the Pelagic Ecosystem of the Black Sea

During recent decades, the Black Sea has been affected by many negative factors that strongly changed the condition of its ecosystem. Especially trophic relationships in the Black Sea pelagic system became very vulnerable influencing the food supply, productivity and abundance of many species and populations of this marine basin. Food is one of most important link between biota and its environment. In this monograph, the role and variability of trophodynamic processes that effect the well-being (health) of main heterotrophic components of ecosystem were analysed in detail for a few key species as indicators for estimation of ecosystem condition in whole. These are most significant mass species of the Black Sea pelagic ecosystem. Among copepods this is Calanus euxinus that dominates the mesozooplankton which makes up the fodder base of planktivorous fishes. Among gelatinous these are medusa Aurelia aurita and the alien ctenophores Mnemiopsis leidyi and Beroe ovata which affected strongly mesozooplankton composition. Lastly among fishes the anchovy Engraulis encrasicolus ponticus and sprat Sprattus sprattus phalericus that dominate small pelagic fishery. We considered in this monograph: • Diel feeding behaviour, in situ feeding rate of Calanus euxinus and impact of mesozooplankton on primary production and phytoplankton biomass. • The effect of vertical migrations on energy budget and its components in C. euxinus; metabolic substrates used in catabolic processes under both aerobic and hypoxic conditions, the role of reserve lipids and effect of abiotic factors on individual growth and population structure of this species. • The intensity and efficiency of ingestion and energy transformation in three gelatinous species ( jellyfish Aurelia aurita, ctenophores Mnemiopsis leidyi and Beroe ovata) and their predatory impact on zooplankton community. • Nutritional condition and food supply of anchovy and sprat in the close interaction with natural biotic and abiotic and anthropogenic factors. • Tendencies in this interaction during long time space: since 1960 s till present years. • Estimation of population condition of these species and its long-term change. This monograph is the collective work of Ukrainian and Turkish scientists studying complex hydrobiological problems of the Black Sea. Its aim is to reveal the significance of nutritional factors on the ecology of Black Sea biota, including changes which have already occurred, as well as offering some insight into changes that may happen in the future. Our joint investigations started in the first half of the 1990s, when conditions for the close cooperation of researchers from the two countries were suitable after the collapse of the Soviet era. This spirit continues to the present day. Professor Ümit Unluata, Director of Erdemli Institute of Marine Sciences (Middle East Technical University, Ankara) was of paramount importance in organising and fostering the work undertaken. We would like to devote this monograph to the memory of him, who died so prematurely. We are also grateful to Academician Professor V. N. Eremeev, Director of the Sevastopol Institute of Biology of the Southern Sea (National Academy of Sciences of Ukraine), and to the directors of Erdemli Institute of Marine Sciences (Professor Ilkay Salihoglu, Professor Sukru Besiktepe and Professor Ferit Bingel) who also made significant contributions to the Ukrainian–Turkish collaboration. We are grateful to Dr Bill Parr from the Black Sea Ecosystem Recovery Project for his valuable efforts in improving earlier drafts. All these investigations were carried out within the framework of the following five NATO linkage-grants: • Pelagic animal food supply in the unstable Black Sea environment, • Will the new alien ctenophore Beroe ovata control the plankton community in the Black Sea? • Grazing, growth and production of Calanus euxinus in the Black Sea, • Bioindicators for assessment of Black Sea ecosystem recovery, • Adaptability and vulnerability of marine species in changing environments. And four TUBITAK - NASU joint projects: • Quantification of the recent ctenophore invader Beroe ovata impact in the Black Sea • Monitoring of the Black Sea anchovy and sprat, • Salinity tolerance as a key factor of invasion success of the copepods of Calanus genus into the Sea of Marmara, • Salinity tolerance as a key factor of invasion success of the mesozooplankton species into the Sea of Marmara. We hope that this publication will make a substantial contribution to future studies of the Black Sea ecosystem and offers further understanding of those features regulating biological processes in this unique marine basin

Greenberger-Horne-Zeilinger-like proof of Bell's theorem involving observers who do not share a reference frame

Vaidman described how a team of three players, each of them isolated in a remote booth, could use a three-qubit Greenberger-Horne-Zeilinger state to always win a game which would be impossible to always win without quantum resources. However, Vaidman's method requires all three players to share a common reference frame; it does not work if the adversary is allowed to disorientate one player. Here we show how to always win the game, even if the players do not share any reference frame. The introduced method uses a 12-qubit state which is invariant under any transformation $R_a \otimes R_b \otimes R_c$ (where $R_a = U_a \otimes U_a \otimes U_a \otimes U_a$, where $U_j$ is a unitary operation on a single qubit) and requires only single-qubit measurements. A number of further applications of this 12-qubit state are described.Comment: REVTeX4, 6 pages, 1 figur

Bell inequalities and distillability in N-quantum-bit systems

The relation between Bell inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of any of these inequalities by a quantum state implies that pure-state entanglement can be distilled from it. The corresponding distillation protocol may require that some of the parties join into several groups. We show that there exists a link between the amount of the Bell inequality violation and the size of the groups they have to form for distillation. Thus, a strong violation is always sufficient for full N-partite distillability. This result also allows for a security proof of multi-partite quantum key distribution (QKD) protocols.Comment: REVTEX, 12 pages, two figure

Relativistic quantum information and time machines

Relativistic quantum information combines the informational approach to understanding and using quantum mechanics systems - quantum information - with the relativistic view of the universe. In this introductory review we examine key results to emerge from this new field of research in physics and discuss future directions. A particularly active area recently has been the question of what happens when quantum systems interact with general relativistic closed timelike curves - effectively time machines. We discuss two different approaches that have been suggested for modelling such situations. It is argued that the approach based on matching the density operator of the quantum state between the future and past most consistently avoids the paradoxes usually associated with time travel.Comment: to appear in Contemporary Physic