354 research outputs found
Different quantum f-divergences and the reversibility of quantum operations
The concept of classical -divergences gives a unified framework to
construct and study measures of dissimilarity of probability distributions;
special cases include the relative entropy and the R\'enyi divergences. Various
quantum versions of this concept, and more narrowly, the concept of R\'enyi
divergences, have been introduced in the literature with applications in
quantum information theory; most notably Petz' quasi-entropies (standard
-divergences), Matsumoto's maximal -divergences, measured
-divergences, and sandwiched and --R\'enyi divergences.
In this paper we give a systematic overview of the various concepts of
quantum -divergences with a main focus on their monotonicity under quantum
operations, and the implications of the preservation of a quantum
-divergence by a quantum operation. In particular, we compare the standard
and the maximal -divergences regarding their ability to detect the
reversibility of quantum operations. We also show that these two quantum
-divergences are strictly different for non-commuting operators unless
is a polynomial, and obtain some analogous partial results for the relation
between the measured and the standard -divergences.
We also study the monotonicity of the --R\'enyi divergences under
the special class of bistochastic maps that leave one of the arguments of the
R\'enyi divergence invariant, and determine domains of the parameters
where monotonicity holds, and where the preservation of the
--R\'enyi divergence implies the reversibility of the quantum
operation.Comment: 70 pages. v4: New Proposition 3.8 and Appendix D on the continuity
properties of the standard f-divergences. The 2-positivity assumption removed
from Theorem 3.34. The achievability of the measured f-divergence is shown in
Proposition 4.17, and Theorem 4.18 is updated accordingl
Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions
There are different inequivalent ways to define the R\'enyi capacity of a
channel for a fixed input distribution . In a 1995 paper Csisz\'ar has shown
that for classical discrete memoryless channels there is a distinguished such
quantity that has an operational interpretation as a generalized cutoff rate
for constant composition channel coding. We show that the analogous notion of
R\'enyi capacity, defined in terms of the sandwiched quantum R\'enyi
divergences, has the same operational interpretation in the strong converse
problem of classical-quantum channel coding. Denoting the constant composition
strong converse exponent for a memoryless classical-quantum channel with
composition and rate as , our main result is that where is the -weighted sandwiched R\'enyi
divergence radius of the image of the channel.Comment: 46 pages. V7: Added the strong converse exponent with cost constrain
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The Performativity of Literature Reviewing: Constituting the Corporate Social Responsibility Literature through Re-Presentation and Intervention
Although numerous books and articles provide toolkit approaches to explain how to conduct literature reviews, these prescriptions regard literature reviewing as the production of representations of academic fields. Such representationalism is rarely questioned. Building on insights from social studies of science, we conceptualize literature reviewing as a performative endeavor that co-constitutes the literature it is supposed to “neutrally” describe, through a dual movement of re-presenting—constructing an account different from the literature, and intervening—adding to and potentially shaping this literature. We discuss four problems inherent to this movement of performativity—description, explicitness, provocation, and simulacrum—and then explore them through a systematic review of 48 reviews of the literature on Corporate Social Responsibility (CSR) for the period 1975-2019. We provide evidence for the performative role of literature reviewing in the CSR field through both re-presenting and intervening. We find that reviews performed the CSR literature and, accordingly, the field’s boundaries, categories, priorities in a self-sustaining manner. By reflexively subjecting our own systematic review to the four performative problems we discuss, we also derive implications of performative analysis for the practice of literature reviewing
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
Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication
This paper studies the difficulty of discriminating between an arbitrary
quantum channel and a "replacer" channel that discards its input and replaces
it with a fixed state. We show that, in this particular setting, the most
general adaptive discrimination strategies provide no asymptotic advantage over
non-adaptive tensor-power strategies. This conclusion follows by proving a
quantum Stein's lemma for this channel discrimination setting, showing that a
constant bound on the Type I error leads to the Type II error decreasing to
zero exponentially quickly at a rate determined by the maximum relative entropy
registered between the channels. The strong converse part of the lemma states
that any attempt to make the Type II error decay to zero at a rate faster than
the channel relative entropy implies that the Type I error necessarily
converges to one. We then refine this latter result by identifying the optimal
strong converse exponent for this task. As a consequence of these results, we
can establish a strong converse theorem for the quantum-feedback-assisted
capacity of a channel, sharpening a result due to Bowen. Furthermore, our
channel discrimination result demonstrates the asymptotic optimality of a
non-adaptive tensor-power strategy in the setting of quantum illumination, as
was used in prior work on the topic. The sandwiched Renyi relative entropy is a
key tool in our analysis. Finally, by combining our results with recent results
of Hayashi and Tomamichel, we find a novel operational interpretation of the
mutual information of a quantum channel N as the optimal type II error exponent
when discriminating between a large number of independent instances of N and an
arbitrary "worst-case" replacer channel chosen from the set of all replacer
channels.Comment: v3: 35 pages, 4 figures, accepted for publication in Communications
in Mathematical Physic
In vitro regeneráció és szaporodás különleges útja Spathiphyllum hibridek esetén = In vitro regeneration and proliferation of Spathiphyllum hybrids through a special way
Contact metamorphic processes on metamorphic xenoliths in neogene intrusive bodies from Southern part of Rodna mountains (East Carpathians, Romania)
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