18,201 research outputs found
First eigenvalue of the -Laplace operator along the Ricci flow
In this paper, we mainly investigate continuity, monotonicity and
differentiability for the first eigenvalue of the -Laplace operator along
the Ricci flow on closed manifolds. We show that the first -eigenvalue is
strictly increasing and differentiable almost everywhere along the Ricci flow
under some curvature assumptions. In particular, for an orientable closed
surface, we construct various monotonic quantities and prove that the first
-eigenvalue is differentiable almost everywhere along the Ricci flow without
any curvature assumption, and therefore derive a -eigenvalue comparison-type
theorem when its Euler characteristic is negative.Comment: 28 pages, added statements and references, deleted verbose statements
and corrected typo
Geometric Steering Criterion for Two-qubit States
According to the geometric characterization of measurement assemblages and
local hidden state (LHS) models, we propose a steering criterion which is both
necessary and sufficient for two-qubit states under arbitrary measurement sets.
A quantity is introduced to describe the required local resources to
reconstruct a measurement assemblage for two-qubit states. We show that the
quantity can be regarded as a quantification of steerability and be used to
find out optimal LHS models. Finally we propose a method to generate
unsteerable states, and construct some two-qubit states which are entangled but
unsteerable under all projective measurements
Characterizing Nonlocal Correlations via Universal Uncertainty Relations
Characterization and certification of nonlocal correlations is one of the the
central topics in quantum information theory. In this work, we develop the
detection methods of entanglement and steering based on the universal
uncertainty relations and fine-grained uncertainty relations. In the course of
our study, the uncertainty relations are formulated in majorization form, and
the uncertainty quantifier can be chosen as any convex Schur concave functions,
this leads to a large set of inequalities, including all existing criteria
based on entropies. We address the question that if all steerable states (or
entangled states) can be witnessed by some uncertainty-based inequality, we
find that for pure states and many important families of states, this is the
case
Some Spectral Properties and Characterizations of Connected Odd-bipartite Uniform Hypergraphs
A -uniform hypergraph is called odd-bipartite ([5]), if is
even and there exists some proper subset of such that each edge of
contains odd number of vertices in . Odd-bipartite hypergraphs are
generalizations of the ordinary bipartite graphs. We study the spectral
properties of the connected odd-bipartite hypergraphs. We prove that the
Laplacian H-spectrum and signless Laplacian H-spectrum of a connected
-uniform hypergraph are equal if and only if is even and is
odd-bipartite. We further give several spectral characterizations of the
connected odd-bipartite hypergraphs. We also give a characterization for a
connected -uniform hypergraph whose Laplacian spectral radius and signless
Laplacian spectral radius are equal, thus provide an answer to a question
raised in [9]. By showing that the Cartesian product of two
odd-bipartite -uniform hypergraphs is still odd-bipartite, we determine that
the Laplacian spectral radius of is the sum of the Laplacian spectral
radii of and , when and are both connected odd-bipartite.Comment: 16 page
Monogamy Relation in No-disturbance Theories
The monogamy is a fundamental property of Bell nonlocality and contextuality.
In this article, we studied the -cycle noncontextual inequalities and
generalized CHSH inequalities in detail and found the sufficient conditions for
those inequalities to be hold. According to those conditions, we provide
several kind of tradeoff relations: monogamy of generalized Bell inequalities
in non-signaling framework, monogamy of cycle type noncontextual inequalities
and monogamy between Bell inequality and noncontextual inequality in general
no-disturbance framework. At last, some generic tradeoff relations of
generalized CHSH inequalities for -party physical systems, which are beyond
one-to-many scenario, are discussed
Geometric Local Hidden State Model for Some Two-qubit States
Adopting the geometric description of steering assemblages and local hidden
states (LHS) model, we construct the optimal LHS model for some two-qubit
states under continuous projective measurements, and obtain a sufficient
steering criterion for all two-qubit states. Using the criterion, we show more
two-qubit states that are asymmetric in steering scenario under projective
measurements. Then we generalize the geometric description into higher
dimensional bipartite cases, calculate the steering bound of two-qutrit
isotropic states and make discussion on more general cases
Hierarchy of Genuine Multipartite Quantum Correlations
Classifying states which exhibiting different statistical correlations is
among the most important problems in quantum information science and quantum
many-body physics. In bipartite case, there is a clear hierarchy of states with
different correlations: total correlation (T) discord (D)
entanglement (E) steering (S)
Bell~nonlocality (NL). However, very little is known about genuine multipartite
correlations (GM) for both conceptual and technical difficulties.
In this work, we show that, for any -partite qudit states, there also exist
such a hierarchy: genuine multipartite total correlations (GMT)
genuine multipartite discord (GMD) genuine multipartite
entanglement (GME) genuine multipartite steering (GMS)
genuine multipartite nonlocality (GMNL). Furthermore, by constructing precise
states, we show that GMT, GME and GMS are inequivalent with each other, thus
GMT GME GMS
Entropic No-Disturbance as a Physical Principle
The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum
mechanics does not present the property of realism, the essence of the theorem
is the lack of a joint probability distributions for some experiment settings.
In this work, we exploit the information theoretic form of the theorem using
information measure instead of probabilistic measure and indicate that quantum
mechanics does not present such entropic realism neither. The entropic form of
Gleason's no-disturbance principle is developed and it turns out to be
characterized by the intersection of several entropic cones. Entropic
contextuality and entropic nonlocality are investigated in depth in this
framework. We show how one can construct monogamy relations using entropic cone
and basic Shannon-type inequalities. The general criterion for several entropic
tests to be monogamous is also developed, using the criterion, we demonstrate
that entropic nonlocal correlations are monogamous, entropic contextuality
tests are monogamous and entropic nonlocality and entropic contextuality are
also monogamous. Finally, we analyze the entropic monogamy relations for
multiparty and many-test case, which plays a crucial role in quantum network
communication
Assertion-Based Design Exploration of DVS in Network Processor Architectures
With the scaling of technology and higher requirements on performance and
functionality, power dissipation is becoming one of the major design
considerations in the development of network processors. In this paper, we use
an assertion-based methodology for system-level power/performance analysis to
study two dynamic voltage scaling (DVS) techniques, traffic-based DVS and
execution-based DVS, in a network processor model. Using the automatically
generated distribution analyzers, we analyze the power and performance
distributions and study their trade-offs for the two DVS policies with
different parameter settings such as threshold values and window sizes. We
discuss the optimal configurations of the two DVS policies under different
design requirements. By a set of experiments, we show that the assertion-based
trace analysis methodology is an efficient tool that can help a designer easily
compare and study optimal architectural configurations in a large design space.Comment: Submitted on behalf of EDAA (http://www.edaa.com/
An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer Code
An efficient algorithm for constructing restricted Boltzmann machine (RBM)
architecture of arbitrary stabilizer group is presented. Some partial results
of this problem have been given in arXiv:1802.03738, in this work we give a
complete solution via a different approach. We show that by transforming a
stabilizer group into the standard form, every stabilizer code state can be
efficiently represented by RBM architecture and we can explicitly get the RBM
parameters in this algorithmic way
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