Instantaneous measurement of non-local variables

It is shown, under the assumption of possibility to perform an arbitrary local operation, that all nonlocal variables related to two or more separate sites can be measured instantaneously, except for a finite time required for bringing to one location the classical records from these sites which yield the result of the measurement. It is a verification measurement: it yields reliably the eigenvalues of the nonlocal variables, but it does not prepare the eigenstates of the system.Comment: 4 pages, revised version, to be published in PR

A unified mechanistic model of niche, neutrality and violation of the competitive exclusion principle

The origin of species richness is one of the most widely discussed questions in ecology. The absence of unified mechanistic model of competition makes difficult our deep understanding of this subject. Here we show such a two-species competition model that unifies (i) a mechanistic niche model, (ii) a mechanistic neutral (null) model and (iii) a mechanistic violation of the competitive exclusion principle. Our model is an individual-based cellular automaton. We demonstrate how two trophically identical and aggressively propagating species can stably coexist in one stable homogeneous habitat without any trade-offs in spite of their 10% difference in fitness. Competitive exclusion occurs if the fitness difference is significant (approximately more than 30%). If the species have one and the same fitness they stably coexist and have similar numbers. We conclude that this model shows diffusion-like and half-soliton-like mechanisms of interactions of colliding population waves. The revealed mechanisms eliminate the existing contradictions between ideas of niche, neutrality and cases of violation of the competitive exclusion principle

Strong violation of the competitive exclusion principle

Bacteria and plants are able to form population waves as a result of their consumer behaviour and propagation. A soliton-like interpenetration of colliding population waves was assumed but not proved earlier. Here we show how and why colliding population waves of trophically identical but fitness different species can interpenetrate through each other without delay. We have hypothesized and revealed here that the last mechanism provides a stable coexistence of two, three and four species, competing for the same limiting resource in the small homogeneous habitat under constant conditions and without any fitness trade-offs. We have explained the mystery of biodiversity mechanistically because (i) our models are bottom-up mechanistic, (ii) the revealed interpenetration mechanism provides strong violation of the competitive exclusion principle and (iii) we have shown that the increase in the number of competing species increases the number of cases of coexistence. Thus the principled assumptions of fitness neutrality (equivalence), competitive trade-offs and competitive niches are redundant for fundamental explanation of species richness

Inter-Tunneling Mechanism of Colliding Population Waves

Here we show a new interaction mechanism of colliding population waves. It provides a stable coexistence of two similar but different species competing for the same limiting resource during their asexual propagation in a limited homogeneous environment under constant conditions. The revealed mechanism opens new opportunities in conservation biology

Strong and weak competitors can coexist in the same niche

The competitive exclusion principle postulates that two trophically identical but fitness different species can not stably coexist in the same niche. However, this principle contradicts the observed nature's species richness. This fact is known as the biodiversity paradox. Here, using a simple cellular automaton model, we mechanistically show how two trophically identical, but fitness different species may stably coexist in the same niche. As environment is stable and any trade-offs are absent in this model, it strongly violates the competitive exclusion principle

The fundamental limit on the rate of quantum dynamics: the unified bound is tight

The question of how fast a quantum state can evolve has attracted a considerable attention in connection with quantum measurement, metrology, and information processing. Since only orthogonal states can be unambiguously distinguished, a transition from a state to an orthogonal one can be taken as the elementary step of a computational process. Therefore, such a transition can be interpreted as the operation of "flipping a qubit", and the number of orthogonal states visited by the system per unit time can be viewed as the maximum rate of operation. A lower bound on the orthogonalization time, based on the energy spread DeltaE, was found by Mandelstam and Tamm. Another bound, based on the average energy E, was established by Margolus and Levitin. The bounds coincide, and can be exactly attained by certain initial states if DeltaE=E; however, the problem remained open of what the situation is otherwise. Here we consider the unified bound that takes into account both DeltaE and E. We prove that there exist no initial states that saturate the bound if DeltaE is not equal to E. However, the bound remains tight: for any given values of DeltaE and E, there exists a one-parameter family of initial states that can approach the bound arbitrarily close when the parameter approaches its limit value. The relation between the largest energy level, the average energy, and the orthogonalization time is also discussed. These results establish the fundamental quantum limit on the rate of operation of any information-processing system.Comment: 4 pages 1 PS figure Late

A long-lived spin-orbit-coupled degenerate dipolar Fermi gas

We describe the creation of a long-lived spin-orbit-coupled gas of quantum degenerate atoms using the most magnetic fermionic element, dysprosium. Spin-orbit-coupling arises from a synthetic gauge field created by the adiabatic following of degenerate dressed states comprised of optically coupled components of an atomic spin. Because of dysprosium's large electronic orbital angular momentum and large magnetic moment, the lifetime of the gas is limited not by spontaneous emission from the light-matter coupling, as for gases of alkali-metal atoms, but by dipolar relaxation of the spin. This relaxation is suppressed at large magnetic fields due to Fermi statistics. We observe lifetimes up to 400 ms, which exceeds that of spin-orbit-coupled fermionic alkali atoms by a factor of 10-100, and is close to the value obtained from a theoretical model. Elastic dipolar interactions are also observed to influence the Rabi evolution of the spin, revealing an interacting fermionic system. The long lifetime of this weakly interacting spin-orbit-coupled degenerate Fermi gas will facilitate the study of quantum many-body phenomena manifest at longer timescales, with exciting implications for the exploration of exotic topological quantum liquids.Comment: 11 pages, 8 figures, one appendi