4,365 research outputs found
Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way post-processing
We derive a bound for the security of QKD with finite resources under one-way
post-processing, based on a definition of security that is composable and has
an operational meaning. While our proof relies on the assumption of collective
attacks, unconditional security follows immediately for standard protocols like
Bennett-Brassard 1984 and six-states. For single-qubit implementations of such
protocols, we find that the secret key rate becomes positive when at least
N\sim 10^5 signals are exchanged and processed. For any other discrete-variable
protocol, unconditional security can be obtained using the exponential de
Finetti theorem, but the additional overhead leads to very pessimistic
estimates
Device independent quantum key distribution secure against coherent attacks with memoryless measurement devices
Device independent quantum key distribution aims to provide a higher degree
of security than traditional QKD schemes by reducing the number of assumptions
that need to be made about the physical devices used. The previous proof of
security by Pironio et al. applies only to collective attacks where the state
is identical and independent and the measurement devices operate identically
for each trial in the protocol. We extend this result to a more general class
of attacks where the state is arbitrary and the measurement devices have no
memory. We accomplish this by a reduction of arbitrary adversary strategies to
qubit strategies and a proof of security for qubit strategies based on the
previous proof by Pironio et al. and techniques adapted from Renner.Comment: 13 pages. Expanded main proofs with more detail, miscellaneous edits
for clarit
Generalized Entropies
We study an entropy measure for quantum systems that generalizes the von
Neumann entropy as well as its classical counterpart, the Gibbs or Shannon
entropy. The entropy measure is based on hypothesis testing and has an elegant
formulation as a semidefinite program, a type of convex optimization. After
establishing a few basic properties, we prove upper and lower bounds in terms
of the smooth entropies, a family of entropy measures that is used to
characterize a wide range of operational quantities. From the formulation as a
semidefinite program, we also prove a result on decomposition of hypothesis
tests, which leads to a chain rule for the entropy.Comment: 21 page
Classification of Reductive Monoid Spaces Over an Arbitrary Field
In this semi-expository paper we review the notion of a spherical space. In
particular we present some recent results of Wedhorn on the classification of
spherical spaces over arbitrary fields. As an application, we introduce and
classify reductive monoid spaces over an arbitrary field.Comment: This is the final versio
On low-sampling-rate Kramers-Moyal coefficients
We analyze the impact of the sampling interval on the estimation of
Kramers-Moyal coefficients. We obtain the finite-time expressions of these
coefficients for several standard processes. We also analyze extreme situations
such as the independence and no-fluctuation limits that constitute useful
references. Our results aim at aiding the proper extraction of information in
data-driven analysis.Comment: 9 pages, 4 figure
Secure certification of mixed quantum states with application to two-party randomness generation
We investigate sampling procedures that certify that an arbitrary quantum
state on subsystems is close to an ideal mixed state
for a given reference state , up to errors on a few positions. This
task makes no sense classically: it would correspond to certifying that a given
bitstring was generated according to some desired probability distribution.
However, in the quantum case, this is possible if one has access to a prover
who can supply a purification of the mixed state.
In this work, we introduce the concept of mixed-state certification, and we
show that a natural sampling protocol offers secure certification in the
presence of a possibly dishonest prover: if the verifier accepts then he can be
almost certain that the state in question has been correctly prepared, up to a
small number of errors.
We then apply this result to two-party quantum coin-tossing. Given that
strong coin tossing is impossible, it is natural to ask "how close can we get".
This question has been well studied and is nowadays well understood from the
perspective of the bias of individual coin tosses. We approach and answer this
question from a different---and somewhat orthogonal---perspective, where we do
not look at individual coin tosses but at the global entropy instead. We show
how two distrusting parties can produce a common high-entropy source, where the
entropy is an arbitrarily small fraction below the maximum (except with
negligible probability)
Tight Finite-Key Analysis for Quantum Cryptography
Despite enormous progress both in theoretical and experimental quantum
cryptography, the security of most current implementations of quantum key
distribution is still not established rigorously. One of the main problems is
that the security of the final key is highly dependent on the number, M, of
signals exchanged between the legitimate parties. While, in any practical
implementation, M is limited by the available resources, existing security
proofs are often only valid asymptotically for unrealistically large values of
M. Here, we demonstrate that this gap between theory and practice can be
overcome using a recently developed proof technique based on the uncertainty
relation for smooth entropies. Specifically, we consider a family of
Bennett-Brassard 1984 quantum key distribution protocols and show that security
against general attacks can be guaranteed already for moderate values of M.Comment: 11 pages, 2 figure
Tunneling Study of the Charge-Ordering Gap on the Surface of LaPrCaMnO Thin Films
Variable temperature scanning tunneling microscopy/spectroscopy studies on
(110) oriented epitaxial thin films of
LaPrCaMnO are reported in the temperature
range of 77 to 340 K. The films, grown on lattice matched NdGaO substrates,
show a hysteretic metal-insulator transition in resistivity at 170 K. The
topographic STM images show step-terrace morphology while the conductance
images display a nearly homogeneous surface. The normalized conductance spectra
at low temperatures (T150 K) show an energy gap of 0.5 eV while for
T180 K a gap of 0.16 eV is found from the activated behavior of the zero
bias conductance. The presence of energy gap and the absence of phase
separation on the surface over more than 2 m2 m area
contradicts the metallic behavior seen in resistivity measurements at low
temperatures. We discuss the measured energy gap in terms of the stabilization
of the insulating CO phase at the film surface.Comment: 5 pages, 5 figures To appear in Phys. Rev.
Instability of a Landau Fermi liquid as the Mott insulator is approached
We examine a two-dimensional Fermi liquid with a Fermi surface which touches
the Umklapp surface first at the 4 points as the
electron density is increased. Umklapp processes at the 4 patches near lead the renormalization group equations to scale to strong
coupling resembling the behavior of a 2-leg ladder at half-filling. The
incompressible character of the fixed point causes a breakdown of Landau theory
at these patches. A further increase in density spreads the incompressible
regions so that the open Fermi surface shrinks to 4 disconnected segments. This
non-Landau state, in which parts of the Fermi surface are truncated to form an
insulating spin liquid, has many features in common with phenomenological
models recently proposed for the cuprate superconductors.Comment: Minor changes. LaTeX2e, 12 pages, 5 figures. J. Phys. CM 10 (1998)
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