The structure of Renyi entropic inequalities

We investigate the universal inequalities relating the alpha-Renyi entropies of the marginals of a multi-partite quantum state. This is in analogy to the same question for the Shannon and von Neumann entropy (alpha=1) which are known to satisfy several non-trivial inequalities such as strong subadditivity. Somewhat surprisingly, we find for 0<alpha<1, that the only inequality is non-negativity: In other words, any collection of non-negative numbers assigned to the nonempty subsets of n parties can be arbitrarily well approximated by the alpha-entropies of the 2^n-1 marginals of a quantum state. For alpha>1 we show analogously that there are no non-trivial homogeneous (in particular no linear) inequalities. On the other hand, it is known that there are further, non-linear and indeed non-homogeneous, inequalities delimiting the alpha-entropies of a general quantum state. Finally, we also treat the case of Renyi entropies restricted to classical states (i.e. probability distributions), which in addition to non-negativity are also subject to monotonicity. For alpha different from 0 and 1 we show that this is the only other homogeneous relation.Comment: 15 pages. v2: minor technical changes in Theorems 10 and 1

Infinitely many constrained inequalities for the von Neumann entropy

We exhibit infinitely many new, constrained inequalities for the von Neumann entropy, and show that they are independent of each other and the known inequalities obeyed by the von Neumann entropy (basically strong subadditivity). The new inequalities were proved originally by Makarychev et al. [Commun. Inf. Syst., 2(2):147-166, 2002] for the Shannon entropy, using properties of probability distributions. Our approach extends the proof of the inequalities to the quantum domain, and includes their independence for the quantum and also the classical cases.Comment: 11 page

The entangling and disentangling power of unitary transformations are unequal

We consider two capacity quantities associated with bipartite unitary gates: the entangling and the disentangling power. For two-qubit unitaries these two capacities are always the same. Here we prove that these capacities are different in general. We do so by constructing an explicit example of a qubit-qutrit unitary whose entangling power is maximal (2 ebits), but whose disentangling power is strictly less. A corollary is that there can be no unique ordering for unitary gates in terms of their ability to perform non-local tasks. Finally we show that in large dimensions, almost all bipartite unitaries have entangling and disentangling capacities close to the maximal possible (and thus in high dimensions the difference in these capacities is small for almost all unitaries).Comment: 6 pages, 1 airfoi

Inequalities for the Ranks of Quantum States

We investigate relations between the ranks of marginals of multipartite quantum states. These are the Schmidt ranks across all possible bipartitions and constitute a natural quantification of multipartite entanglement dimensionality. We show that there exist inequalities constraining the possible distribution of ranks. This is analogous to the case of von Neumann entropy (\alpha-R\'enyi entropy for \alpha=1), where nontrivial inequalities constraining the distribution of entropies (such as e.g. strong subadditivity) are known. It was also recently discovered that all other \alpha-R\'enyi entropies for $\alpha\in(0,1)\cup(1,\infty)$ satisfy only one trivial linear inequality (non-negativity) and the distribution of entropies for $\alpha\in(0,1)$ is completely unconstrained beyond non-negativity. Our result resolves an important open question by showing that also the case of \alpha=0 (logarithm of the rank) is restricted by nontrivial linear relations and thus the cases of von Neumann entropy (i.e., \alpha=1) and 0-R\'enyi entropy are exceptionally interesting measures of entanglement in the multipartite setting

No quantum advantage for nonlocal computation

We investigate the problem of "nonlocal" computation, in which separated parties must compute a function with nonlocally encoded inputs and output, such that each party individually learns nothing, yet together they compute the correct function output. We show that the best that can be done classically is a trivial linear approximation. Surprisingly, we also show that quantum entanglement provides no advantage over the classical case. On the other hand, generalized (i.e. super-quantum) nonlocal correlations allow perfect nonlocal computation. This gives new insights into the nature of quantum nonlocality and its relationship to generalised nonlocal correlations.Comment: 4 page

Neuroimaging in Psychiatry: From Bench to Bedside

This perspective considers the present and the future role of different neuroimaging techniques in the field of psychiatry. After identifying shortcomings of the mainly symptom-focussed diagnostic processes and treatment decisions in modern psychiatry, we suggest topics where neuroimaging methods have the potential to help. These include better understanding of the pathophysiology, improved diagnoses, assistance in therapeutic decisions and the supervision of treatment success by direct assessment of improvement in disease-related brain functions. These different questions are illustrated by examples from neuroimaging studies, with a focus on severe mental and neuropsychiatric illnesses such as schizophrenia and depression. Despite all reservations addressed in the article, we are optimistic that neuroimaging has a huge potential with regard to the above-mentioned questions. We expect that neuroimaging will play an increasing role in the future refinement of the diagnostic process and aid in the development of new therapies in the field of psychiatry

A new inequality for the von Neumann entropy

Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality for the von Neumann entropy which we prove is independent of strong subadditivity: it is an inequality which is true for any four party quantum state, provided that it satisfies three linear relations (constraints) on the entropies of certain reduced states.Comment: 8 pages, 1 eps figur

European ducks in a changing world: human impacts, population processes and species interactions

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Declining peatland bird numbers are not consistent with the increasing Common Crane population

The Common Crane (Grus grus) population has experienced an unprecedented increase across Europe during the last decades. Although cranes feed mostly on invertebrates, amphibians and berries during the breeding season, they can also eat eggs and young of other birds. Therefore, conservationists have raised concerns about the potential predatory effect of cranes on wetland avifauna, but the effects of crane predation on bird numbers have so far not been investigated. We here test the relationship between the crane and peatland bird population' abundances in Finland for five common wader and passerine species, and a set of seven less common waders, using line-transect data spanning from 1987 to 2014. We found that the population densities of two small passerines (Meadow Pipit Anthus pratensis and Western Yellow Wagtail Motacilla flava) and one wader species (Wood Sandpiper Tringa glareola) were positively associated with crane numbers, probably related to a protective effect against nest predators. For the two other common species and the set of less common waders, we did not find any significant relationships with crane abundance. None of the species was influenced by the (lagged) effect of crane presence (i.e. years since crane was first observed). Peatland drainage was responsible for most species' negative densities, indicating the need to protect and restore peatlands to mitigate the loss of peatland bird diversity in Finland. In addition, openness, wetness and area size were important peatland characteristics positively influencing most of the studied bird populations. The development in crane and other mire bird numbers in Europe should be monitored regularly to reveal any possible future predatory effects contributing to the shaping of the peatland bird community.Peer reviewe