1,298 research outputs found
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 satisfy only one trivial linear
inequality (non-negativity) and the distribution of entropies for
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
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
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