8,935 research outputs found
Discrete Fourier analysis with lattices on planar domains
A discrete Fourier analysis associated with translation lattices is developed
recently by the authors. It permits two lattices, one determining the integral
domain and the other determining the family of exponential functions. Possible
choices of lattices are discussed in the case of lattices that tile \RR^2 and
several new results on cubature and interpolation by trigonometric, as well as
algebraic, polynomials are obtained
The Buffered \pi-Calculus: A Model for Concurrent Languages
Message-passing based concurrent languages are widely used in developing
large distributed and coordination systems. This paper presents the buffered
-calculus --- a variant of the -calculus where channel names are
classified into buffered and unbuffered: communication along buffered channels
is asynchronous, and remains synchronous along unbuffered channels. We show
that the buffered -calculus can be fully simulated in the polyadic
-calculus with respect to strong bisimulation. In contrast to the
-calculus which is hard to use in practice, the new language enables easy
and clear modeling of practical concurrent languages. We encode two real-world
concurrent languages in the buffered -calculus: the (core) Go language and
the (Core) Erlang. Both encodings are fully abstract with respect to weak
bisimulations
Complete Characterization of the Ground Space Structure of Two-Body Frustration-Free Hamiltonians for Qubits
The problem of finding the ground state of a frustration-free Hamiltonian
carrying only two-body interactions between qubits is known to be solvable in
polynomial time. It is also shown recently that, for any such Hamiltonian,
there is always a ground state that is a product of single- or two-qubit
states. However, it remains unclear whether the whole ground space is of any
succinct structure. Here, we give a complete characterization of the ground
space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a
span of tree tensor network states of the same tree structure. This
characterization allows us to show that the problem of determining the ground
state degeneracy is as hard as, but no harder than, its classical analog.Comment: 5pages, 3 figure
Symmetric Extension of Two-Qubit States
Quantum key distribution uses public discussion protocols to establish shared
secret keys. In the exploration of ultimate limits to such protocols, the
property of symmetric extendibility of underlying bipartite states
plays an important role. A bipartite state is symmetric extendible
if there exits a tripartite state , such that the marginal
state is identical to the marginal state, i.e. .
For a symmetric extendible state , the first task of the public
discussion protocol is to break this symmetric extendibility. Therefore to
characterize all bi-partite quantum states that possess symmetric extensions is
of vital importance. We prove a simple analytical formula that a two-qubit
state admits a symmetric extension if and only if
\tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}. Given the
intimate relationship between the symmetric extension problem and the quantum
marginal problem, our result also provides the first analytical necessary and
sufficient condition for the quantum marginal problem with overlapping
marginals.Comment: 10 pages, no figure. comments are welcome. Version 2: introduction
rewritte
Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions
Algebraic and fast algebraic attacks are power tools to analyze stream
ciphers. A class of symmetric Boolean functions with maximum algebraic immunity
were found vulnerable to fast algebraic attacks at EUROCRYPT'06. Recently, the
notion of AAR (algebraic attack resistant) functions was introduced as a
unified measure of protection against both classical algebraic and fast
algebraic attacks. In this correspondence, we first give a decomposition of
symmetric Boolean functions, then we show that almost all symmetric Boolean
functions, including these functions with good algebraic immunity, behave badly
against fast algebraic attacks, and we also prove that no symmetric Boolean
functions are AAR functions. Besides, we improve the relations between
algebraic degree and algebraic immunity of symmetric Boolean functions.Comment: 13 pages, submitted to IEEE Transactions on Information Theor
A Theory for Valiant's Matchcircuits (Extended Abstract)
The computational function of a matchgate is represented by its character
matrix. In this article, we show that all nonsingular character matrices are
closed under matrix inverse operation, so that for every , the nonsingular
character matrices of -bit matchgates form a group, extending the recent
work of Cai and Choudhary (2006) of the same result for the case of , and
that the single and the two-bit matchgates are universal for matchcircuits,
answering a question of Valiant (2002)
Cryptanalysis of a multi-party quantum key agreement protocol with single particles
Recently, Sun et al. [Quant Inf Proc DOI: 10.1007/s11128-013-0569-x]
presented an efficient multi-party quantum key agreement (QKA) protocol by
employing single particles and unitary operations. The aim of this protocol is
to fairly and securely negotiate a secret session key among parties with a
high qubit efficiency. In addition, the authors claimed that no participant can
learn anything more than his/her prescribed output in this protocol, i.e., the
sub-secret keys of the participants can be kept secret during the protocol.
However, here we points out that the sub-secret of a participant in Sun et
al.'s protocol can be eavesdropped by the two participants next to him/her. In
addition, a certain number of dishonest participants can fully determine the
final shared key in this protocol. Finally, we discuss the factors that should
be considered when designing a really fair and secure QKA protocol.Comment: 7 page
Probably Safe or Live
This paper presents a formal characterisation of safety and liveness
properties \`a la Alpern and Schneider for fully probabilistic systems. As for
the classical setting, it is established that any (probabilistic tree) property
is equivalent to a conjunction of a safety and liveness property. A simple
algorithm is provided to obtain such property decomposition for flat
probabilistic CTL (PCTL). A safe fragment of PCTL is identified that provides a
sound and complete characterisation of safety properties. For liveness
properties, we provide two PCTL fragments, a sound and a complete one. We show
that safety properties only have finite counterexamples, whereas liveness
properties have none. We compare our characterisation for qualitative
properties with the one for branching time properties by Manolios and Trefler,
and present sound and complete PCTL fragments for characterising the notions of
strong safety and absolute liveness coined by Sistla
State succinctness of two-way finite automata with quantum and classical states
{\it Two-way quantum automata with quantum and classical states} (2QCFA) were
introduced by Ambainis and Watrous in 2002. In this paper we study state
succinctness of 2QCFA.
For any and any , we show that:
{enumerate} there is a promise problem which can be solved by a
2QCFA with one-sided error in a polynomial expected running time
with a constant number (that depends neither on nor on ) of
quantum states and classical states,
whereas the sizes of the corresponding {\it deterministic finite automata}
(DFA), {\it two-way nondeterministic finite automata} (2NFA) and polynomial
expected running time {\it two-way probabilistic finite automata} (2PFA) are at
least , , and , respectively; there
exists a language over the alphabet
which can be recognized by a 2QCFA with one-sided error
in an exponential expected running time with a constant number of
quantum states and classical states,
whereas the sizes of the corresponding DFA, 2NFA and polynomial expected
running time 2PFA are at least , , and ,
respectively; {enumerate} where is a constant.Comment: 26pages, comments and suggestions are welcom
Discrete Fourier Analysis and Chebyshev Polynomials with Group
The discrete Fourier analysis on the
-- triangle is deduced from the
corresponding results on the regular hexagon by considering functions invariant
under the group , which leads to the definition of four families
generalized Chebyshev polynomials. The study of these polynomials leads to a
Sturm-Liouville eigenvalue problem that contains two parameters, whose
solutions are analogues of the Jacobi polynomials. Under a concept of
-degree and by introducing a new ordering among monomials, these polynomials
are shown to share properties of the ordinary orthogonal polynomials. In
particular, their common zeros generate cubature rules of Gauss type
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