14,113 research outputs found
p-topological and p-regular: dual notions in convergence theory
The natural duality between "topological" and "regular," both considered as
convergence space properties, extends naturally to p-regular convergence
spaces, resulting in the new concept of a p-topological convergence space.
Taking advantage of this duality, the behavior of p-topological and p-regular
convergence spaces is explored, with particular emphasis on the former, since
they have not been previously studied. Their study leads to the new notion of a
neighborhood operator for filters, which in turn leads to an especially simple
characterization of a topology in terms of convergence criteria. Applications
include the topological and regularity series of a convergence space.Comment: 12 pages in Acrobat 3.0 PDF forma
A proposal for founding mistrustful quantum cryptography on coin tossing
A significant branch of classical cryptography deals with the problems which
arise when mistrustful parties need to generate, process or exchange
information. As Kilian showed a while ago, mistrustful classical cryptography
can be founded on a single protocol, oblivious transfer, from which general
secure multi-party computations can be built.
The scope of mistrustful quantum cryptography is limited by no-go theorems,
which rule out, inter alia, unconditionally secure quantum protocols for
oblivious transfer or general secure two-party computations. These theorems
apply even to protocols which take relativistic signalling constraints into
account. The best that can be hoped for, in general, are quantum protocols
computationally secure against quantum attack. I describe here a method for
building a classically certified bit commitment, and hence every other
mistrustful cryptographic task, from a secure coin tossing protocol. No
security proof is attempted, but I sketch reasons why these protocols might
resist quantum computational attack.Comment: Title altered in deference to Physical Review's fear of question
marks. Published version; references update
Dissatisfaction with Our Judges
Dissatisfaction with our judges is no new thing. It existed with the United States Supreme Court in the time of Chief Justice MARSHALL, the greatest of American jurists, after the Dred Scott decision, after the conflicting decisions on the power of Congress to make the government notes a legal tender, and at other times. Probably there is no one of the older states where dissatisfaction with the state courts has not been sometimes acute
Efficient quantum key distribution secure against no-signalling eavesdroppers
By carrying out measurements on entangled states, two parties can generate a
secret key which is secure not only against an eavesdropper bound by the laws
of quantum mechanics, but also against a hypothetical "post-quantum"
eavesdroppers limited by the no-signalling principle only. We introduce a
family of quantum key distribution protocols of this type, which are more
efficient than previous ones, both in terms of key rate and noise resistance.
Interestingly, the best protocols involve large number of measurements. We show
that in the absence of noise, these protocols can yield one secret bit per
entanglement bit, implying that the key rates in the no-signalling post-quantum
scenario are comparable to the key rates in usual quantum key distribution.Comment: 11 pages, 2 color figures. v2: minor modifications, added references,
added note on the relation to quant-ph/060604
No Signalling and Quantum Key Distribution
Standard quantum key distribution protocols are provably secure against
eavesdropping attacks, if quantum theory is correct. It is theoretically
interesting to know if we need to assume the validity of quantum theory to
prove the security of quantum key distribution, or whether its security can be
based on other physical principles. The question would also be of practical
interest if quantum mechanics were ever to fail in some regime, because a
scientifically and technologically advanced eavesdropper could perhaps use
post-quantum physics to extract information from quantum communications without
necessarily causing the quantum state disturbances on which existing security
proofs rely. Here we describe a key distribution scheme provably secure against
general attacks by a post-quantum eavesdropper who is limited only by the
impossibility of superluminal signalling. The security of the scheme stems from
violation of a Bell inequality.Comment: Clarifications and minor revisions in response to comments. Final
version; to appear in Phys. Rev. Let
Offering alternatives as a way of issuing directives to children: Putting the worse option last
In a corpus of c. 250 h of recorded interactions between young children and adults in USA and UK households, we found that children could be directed to change their course of action by three syntactic formats that offered alternatives: an imperative, or a modal declarative, plus a consequential alternative to non-compliance (e.g. come down at once or I shall send you straight to bed; you’ve got to stand here with it or it goes back in the cupboard), or an interrogative requiring a preference (e.g. do you want to put them neatly in the corner for mummy please or do you wanna go to bed). Formatted syntactically as or-alternatives, these can perform the actions both of warning and threatening. But they make a ‘bad’ course of action contiguous to the child's turn. We argue that adults choose this format because the interactional preference for contiguity makes the negative alternative the more salient one. This implies that adults attribute to children the ability to appreciate the flouting of preference organisation for deontic effect
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