933 research outputs found
Temporal quantum correlations and Leggett-Garg inequalities in multi-level systems
We show that the quantum bound for temporal correlations in a Leggett-Garg
test, analogous to the Tsirelson bound for spatial correlations in a Bell test,
strongly depends on the number of levels that can be accessed by the
measurement apparatus via projective measurements. We provide exact bounds for
small , that exceed the known bound for the Leggett-Garg inequality, and
show that in the limit the Leggett-Garg inequality can be
violated up to its algebraic maximum.Comment: 6 pages, 2 figure
Theoretical research without projects
We propose a funding scheme for theoretical research that does not rely on
project proposals, but on recent past scientific productivity. Given a
quantitative figure of merit on the latter and the total research budget, we
introduce a number of policies to decide the allocation of funds in each grant
call. Under some assumptions on scientific productivity, some of such policies
are shown to converge, in the limit of many grant calls, to a funding
configuration that is close to the maximum total productivity of the whole
scientific community. We present numerical simulations showing evidence that
these schemes would also perform well in the presence of statistical noise in
the scientific productivity and/or its evaluation. Finally, we prove that one
of our policies cannot be cheated by individual research units. Our work must
be understood as a first step towards a mathematical theory of the research
activity.Comment: Some edits to the published versio
Necessary and sufficient condition for quantum state-independent contextuality
We solve the problem of whether a set of quantum tests reveals
state-independent contextuality and use this result to identify the simplest
set of the minimal dimension. We also show that identifying state-independent
contextuality graphs [R. Ramanathan and P. Horodecki, Phys. Rev. Lett. 112,
040404 (2014)] is not sufficient for revealing state-independent contextuality.Comment: 5 pages, 3 graph
Extreme violation of local realism in quantum hypergraph states
Hypergraph states form a family of multiparticle quantum states that
generalizes the well-known concept of Greenberger-Horne-Zeilinger states,
cluster states, and more broadly graph states. We study the nonlocal properties
of quantum hypergraph states. We demonstrate that the correlations in
hypergraph states can be used to derive various types of nonlocality proofs,
including Hardy-type arguments and Bell inequalities for genuine multiparticle
nonlocality. Moreover, we show that hypergraph states allow for an
exponentially increasing violation of local realism which is robust against
loss of particles. Our results suggest that certain classes of hypergraph
states are novel resources for quantum metrology and measurement-based quantum
computation.Comment: 31 pages, 1 figure, v3: final versio
Leggett-Garg macrorealism and the quantum nondisturbance conditions
We investigate the relation between a refined version of Leggett and Garg
conditions for macrorealism, namely the no-signaling-in-time (NSIT) conditions,
and the quantum mechanical notion of nondisturbance between measurements. We
show that all NSIT conditions are satisfied for any state preparation if and
only if certain compatibility criteria on the state-update rules relative to
the measurements, i.e. quantum instruments, are met. The systematic treatment
of NSIT conditions supported by structural results on nondisturbance provides a
unified framework for the discussion of the the clumsiness loophole. This
extends previous approaches and allows for a tightening of the loophole via a
hierarchy of tests able to disprove a larger class of macrorealist theories.
Finally, we discuss perspectives for a resource theory of quantum mechanical
disturbance related to violations of macrorealism.Comment: Final versio
Bounding temporal quantum correlations
Sequential measurements on a single particle play an important role in
fundamental tests of quantum mechanics. We provide a general method to analyze
temporal quantum correlations, which allows us to compute the maximal
correlations for sequential measurements in quantum mechanics. As an
application, we present the full characterization of temporal correlations in
the simplest Leggett-Garg scenario and in the sequential measurement scenario
associated with the most fundamental proof of the Kochen-Specker theorem.Comment: 8 pages, 2 figure
Notes on Lattice-Based Cryptography
Asymmetrisk kryptering er avhengig av antakelsen om at noen beregningsproblemer er vanskelige å løse. I 1994 viste Peter Shor at de to mest brukte beregningsproblemene, nemlig det diskrete logaritmeproblemet og primtallsfaktorisering, ikke lenger er vanskelige å løse når man bruker en kvantedatamaskin. Siden den gang har forskere jobbet med å finne nye beregningsproblemer som er motstandsdyktige mot kvanteangrep for å erstatte disse to. Gitterbasert kryptografi er forskningsfeltet som bruker kryptografiske primitiver som involverer vanskelige problemer definert på gitter, for eksempel det korteste vektorproblemet og det nærmeste vektorproblemet. NTRU-kryptosystemet, publisert i 1998, var et av de første som ble introdusert på dette feltet. Problemet Learning With Error (LWE) ble introdusert i 2005 av Regev, og det regnes nå som et av de mest lovende beregningsproblemene som snart tas i bruk i stor skala. Å studere vanskelighetsgraden og å finne nye og raskere algoritmer som løser den, ble et ledende forskningstema innen kryptografi.
Denne oppgaven inkluderer følgende bidrag til feltet:
- En ikke-triviell reduksjon av Mersenne Low Hamming Combination Search Problem, det underliggende problemet med et NTRU-lignende kryptosystem, til Integer Linear Programming (ILP). Særlig finner vi en familie av svake nøkler.
- En konkret sikkerhetsanalyse av Integer-RLWE, en vanskelig beregningsproblemvariant av LWE, introdusert av Gu Chunsheng. Vi formaliserer et meet-in-the-middle og et gitterbasert angrep for denne saken, og vi utnytter en svakhet ved parametervalget gitt av Gu, for å bygge et forbedret gitterbasert angrep.
- En forbedring av Blum-Kalai-Wasserman-algoritmen for å løse LWE. Mer spesifikt, introduserer vi et nytt reduksjonstrinn og en ny gjetteprosedyre til algoritmen. Disse tillot oss å utvikle to implementeringer av algoritmen, som er i stand til å løse relativt store LWE-forekomster. Mens den første effektivt bare bruker RAM-minne og er fullt parallelliserbar, utnytter den andre en kombinasjon av RAM og disklagring for å overvinne minnebegrensningene gitt av RAM.
- Vi fyller et tomrom i paringsbasert kryptografi. Dette ved å gi konkrete formler for å beregne hash-funksjon til G2, den andre gruppen i paringsdomenet, for Barreto-Lynn-Scott-familien av paringsvennlige elliptiske kurver.Public-key Cryptography relies on the assumption that some computational problems are hard to solve. In 1994, Peter Shor showed that the two most used computational problems, namely the Discrete Logarithm Problem and the Integer Factoring Problem, are not hard to solve anymore when using a quantum computer. Since then, researchers have worked on finding new computational problems that are resistant to quantum attacks to replace these two. Lattice-based Cryptography is the research field that employs cryptographic primitives involving hard problems defined on lattices, such as the Shortest Vector Problem and the Closest Vector Problem. The NTRU cryptosystem, published in 1998, was one of the first to be introduced in this field. The Learning With Error (LWE) problem was introduced in 2005 by Regev, and it is now considered one of the most promising computational problems to be employed on a large scale in the near future. Studying its hardness and finding new and faster algorithms that solve it became a leading research topic in Cryptology.
This thesis includes the following contributions to the field:
- A non-trivial reduction of the Mersenne Low Hamming Combination Search Problem, the underlying problem of an NTRU-like cryptosystem, to Integer Linear Programming (ILP). In particular, we find a family of weak keys.
- A concrete security analysis of the Integer-RLWE, a hard computational problem variant of LWE introduced by Gu Chunsheng. We formalize a meet-in-the-middle attack and a lattice-based attack for this case, and we exploit a weakness of the parameters choice given by Gu to build an improved lattice-based attack.
- An improvement of the Blum-Kalai-Wasserman algorithm to solve LWE. In particular, we introduce a new reduction step and a new guessing procedure to the algorithm. These allowed us to develop two implementations of the algorithm that are able to solve relatively large LWE instances. While the first one efficiently uses only RAM memory and is fully parallelizable, the second one exploits a combination of RAM and disk storage to overcome the memory limitations given by the RAM.
- We fill a gap in Pairing-based Cryptography by providing concrete formulas to compute hash-maps to G2, the second group in the pairing domain, for the Barreto-Lynn-Scott family of pairing-friendly elliptic curves.Doktorgradsavhandlin
One-to-one mapping between steering and joint measurability problems
Quantum steering refers to the possibility for Alice to remotely steer Bob's
state by performing local measurements on her half of a bipartite system. Two
necessary ingredients for steering are entanglement and incompatibility of
Alice's measurements. In particular, it has been recently proven that for the
case of pure states of maximal Schmidt rank the problem of steerability for
Bob's assemblage is equivalent to the problem of joint measurability for
Alice's observables. We show that such an equivalence holds in general, namely,
the steerability of any assemblage can always be formulated as a joint
measurability problem, and vice versa. We use this connection to introduce
steering inequalities from joint measurability criteria and develop quantifiers
for the incompatibility of measurements.Comment: Definition of the SDP in Eq. (31) corrected, thanks to a comment by
Marco Piani and Benjamin A. Ros
Molecular and enological characterization of autochthonous <i>Saccharomyces cerevisiae</i> strains isolated from grape-musts and wines Cannonau
Fermentation by autochthonous yeasts may produce wines with enological properties that are unique of a specific area or variety of grape must. In order to identify yeast starter strains for the production of the Sardinian wine Cannonau DOC, 66 Saccharomyces cerevisiae strains, isolated from musts and wines Cannonau of six vitivinicole areas in Sardinia, were subjected to enological characterization and molecular identification. The RFLP-PCR fingerprinting of the ITS region of rRNA (ITS1-5,8S- ITS2) as well as ethanol, foam, and H2S production were analysed
Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
In a recent work [Phys. Rev. Lett. 116, 240401 (2016)], a framework known by
the name of "assemblage moment matrices" (AMMs) has been introduced for the
device-independent quantification of quantum steerability and measurement
incompatibility. In other words, even with no assumption made on the
preparation device nor the measurement devices, one can make use of this
framework to certify, directly from the observed data, the aforementioned
quantum features. Here, we further explore the framework of AMM and provide
improved device-independent bounds on the generalized robustness of
entanglement, the incompatibility robustness and the incompatibility weight. We
compare the tightness of our device-independent bounds against those obtained
from other approaches. Along the way, we also provide an analytic form for the
generalized robustness of entanglement for an arbitrary two-qudit isotropic
state. When considering a Bell-type experiment in a tri- or more-partite
scenario, we further show that the framework of AMM provides a natural way to
characterize a superset to the set of quantum correlations, namely, one which
also allows post-quantum steering.Comment: 17 pages, 6 figures. Comments welcome
- …