5,245 research outputs found
Generalizations of Tucker-Fan-Shashkin lemmas
Tucker and Ky Fan's lemma are combinatorial analogs of the Borsuk-Ulam
theorem (BUT). In 1996, Yu. A. Shashkin proved a version of Fan's lemma, which
is a combinatorial analog of the odd mapping theorem (OMT). We consider
generalizations of these lemmas for BUT-manifolds, i.e. for manifolds that
satisfy BUT. Proofs rely on a generalization of the OMT and on a lemma about
the doubling of manifolds with boundaries that are BUT-manifolds.Comment: 10 pages, 2 figure
Matroids and Quantum Secret Sharing Schemes
A secret sharing scheme is a cryptographic protocol to distribute a secret
state in an encoded form among a group of players such that only authorized
subsets of the players can reconstruct the secret. Classically, efficient
secret sharing schemes have been shown to be induced by matroids. Furthermore,
access structures of such schemes can be characterized by an excluded minor
relation. No such relations are known for quantum secret sharing schemes. In
this paper we take the first steps toward a matroidal characterization of
quantum secret sharing schemes. In addition to providing a new perspective on
quantum secret sharing schemes, this characterization has important benefits.
While previous work has shown how to construct quantum secret sharing schemes
for general access structures, these schemes are not claimed to be efficient.
In this context the present results prove to be useful; they enable us to
construct efficient quantum secret sharing schemes for many general access
structures. More precisely, we show that an identically self-dual matroid that
is representable over a finite field induces a pure state quantum secret
sharing scheme with information rate one
Unconditionally Secure Bit Commitment
We describe a new classical bit commitment protocol based on cryptographic
constraints imposed by special relativity. The protocol is unconditionally
secure against classical or quantum attacks. It evades the no-go results of
Mayers, Lo and Chau by requiring from Alice a sequence of communications,
including a post-revelation verification, each of which is guaranteed to be
independent of its predecessor.Comment: Typos corrected. Reference details added. To appear in Phys. Rev.
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Topological fault-tolerance in cluster state quantum computation
We describe a fault-tolerant version of the one-way quantum computer using a
cluster state in three spatial dimensions. Topologically protected quantum
gates are realized by choosing appropriate boundary conditions on the cluster.
We provide equivalence transformations for these boundary conditions that can
be used to simplify fault-tolerant circuits and to derive circuit identities in
a topological manner. The spatial dimensionality of the scheme can be reduced
to two by converting one spatial axis of the cluster into time. The error
threshold is 0.75% for each source in an error model with preparation, gate,
storage and measurement errors. The operational overhead is poly-logarithmic in
the circuit size.Comment: 20 pages, 12 figure
One-way quantum key distribution: Simple upper bound on the secret key rate
We present a simple method to obtain an upper bound on the achievable secret
key rate in quantum key distribution (QKD) protocols that use only
unidirectional classical communication during the public-discussion phase. This
method is based on a necessary precondition for one-way secret key
distillation; the legitimate users need to prove that there exists no quantum
state having a symmetric extension that is compatible with the available
measurements results. The main advantage of the obtained upper bound is that it
can be formulated as a semidefinite program, which can be efficiently solved.
We illustrate our results by analysing two well-known qubit-based QKD
protocols: the four-state protocol and the six-state protocol. Recent results
by Renner et al., Phys. Rev. A 72, 012332 (2005), also show that the given
precondition is only necessary but not sufficient for unidirectional secret key
distillation.Comment: 11 pages, 1 figur
Modes of Foreign Entry under Asymmetric Information about Potential Technology Spillovers
This paper studies the effect of technology spillovers on the entry decision of a multinational enterprise into a foreign market. Two alternative entry modes for a foreign direct investment are considered: Greenfield investment versus acquisition. We find that with quantity competition a spillover makes acquisitions less attractive, while with price competition acquisitions become more attractive. Asymmetric information about potential spillovers always reduces the number of
acquisitions independently of whether the host country or the entrant has private information. Interestingly, we find that asymmetric information always hurts the entrant, while it sometimes is in favor of the host country
Experimental demonstration of phase-remapping attack in a practical quantum key distribution system
Unconditional security proofs of various quantum key distribution (QKD)
protocols are built on idealized assumptions. One key assumption is: the sender
(Alice) can prepare the required quantum states without errors. However, such
an assumption may be violated in a practical QKD system. In this paper, we
experimentally demonstrate a technically feasible "intercept-and-resend" attack
that exploits such a security loophole in a commercial "plug & play" QKD
system. The resulting quantum bit error rate is 19.7%, which is below the
proven secure bound of 20.0% for the BB84 protocol. The attack we utilize is
the phase-remapping attack (C.-H. F. Fung, et al., Phys. Rev. A, 75, 32314,
2007) proposed by our group.Comment: 16 pages, 6 figure
Discovery of the peculiar supernova 1998bw in the error box of GRB980425
The discovery of X-ray, optical and radio afterglows of gamma-ray bursts
(GRBs) and the measurements of the distances to some of them have established
that these events come from Gpc distances and are the most powerful photon
emitters known in the Universe, with peak luminosities up to 10^52 erg/s. We
here report the discovery of an optical transient, in the BeppoSAX Wide Field
Camera error box of GRB980425, which occurred within about a day of the
gamma-ray burst. Its optical light curve, spectrum and location in a spiral arm
of the galaxy ESO 184-G82, at a redshift z = 0.0085, show that the transient is
a very luminous type Ic supernova, SN1998bw. The peculiar nature of SN1998bw is
emphasized by its extraordinary radio properties which require that the radio
emitter expand at relativistical speed. Since SN1998bw is very different from
all previously observed afterglows of GRBs, our discovery raises the
possibility that very different mechanisms may give rise to GRBs, which differ
little in their gamma-ray properties.Comment: Under press embargo at Nature (submitted June 10, 1998
Composability in quantum cryptography
In this article, we review several aspects of composability in the context of
quantum cryptography. The first part is devoted to key distribution. We discuss
the security criteria that a quantum key distribution protocol must fulfill to
allow its safe use within a larger security application (e.g., for secure
message transmission). To illustrate the practical use of composability, we
show how to generate a continuous key stream by sequentially composing rounds
of a quantum key distribution protocol. In a second part, we take a more
general point of view, which is necessary for the study of cryptographic
situations involving, for example, mutually distrustful parties. We explain the
universal composability framework and state the composition theorem which
guarantees that secure protocols can securely be composed to larger
applicationsComment: 18 pages, 2 figure
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