354 research outputs found
Quantum Cryptography Based Solely on Bell's Theorem
Information-theoretic key agreement is impossible to achieve from scratch and
must be based on some - ultimately physical - premise. In 2005, Barrett, Hardy,
and Kent showed that unconditional security can be obtained in principle based
on the impossibility of faster-than-light signaling; however, their protocol is
inefficient and cannot tolerate any noise. While their key-distribution scheme
uses quantum entanglement, its security only relies on the impossibility of
superluminal signaling, rather than the correctness and completeness of quantum
theory. In particular, the resulting security is device independent. Here we
introduce a new protocol which is efficient in terms of both classical and
quantum communication, and that can tolerate noise in the quantum channel. We
prove that it offers device-independent security under the sole assumption that
certain non-signaling conditions are satisfied. Our main insight is that the
XOR of a number of bits that are partially secret according to the
non-signaling conditions turns out to be highly secret. Note that similar
statements have been well-known in classical contexts. Earlier results had
indicated that amplification of such non-signaling-based privacy is impossible
to achieve if the non-signaling condition only holds between events on Alice's
and Bob's sides. Here, we show that the situation changes completely if such a
separation is given within each of the laboratories.Comment: 32 pages, v2: changed introduction, added reference
Renyi Differential Privacy
We propose a natural relaxation of differential privacy based on the Renyi
divergence. Closely related notions have appeared in several recent papers that
analyzed composition of differentially private mechanisms. We argue that the
useful analytical tool can be used as a privacy definition, compactly and
accurately representing guarantees on the tails of the privacy loss.
We demonstrate that the new definition shares many important properties with
the standard definition of differential privacy, while additionally allowing
tighter analysis of composite heterogeneous mechanisms
Computational Extensive-Form Games
We define solution concepts appropriate for computationally bounded players
playing a fixed finite game. To do so, we need to define what it means for a
\emph{computational game}, which is a sequence of games that get larger in some
appropriate sense, to represent a single finite underlying extensive-form game.
Roughly speaking, we require all the games in the sequence to have essentially
the same structure as the underlying game, except that two histories that are
indistinguishable (i.e., in the same information set) in the underlying game
may correspond to histories that are only computationally indistinguishable in
the computational game. We define a computational version of both Nash
equilibrium and sequential equilibrium for computational games, and show that
every Nash (resp., sequential) equilibrium in the underlying game corresponds
to a computational Nash (resp., sequential) equilibrium in the computational
game. One advantage of our approach is that if a cryptographic protocol
represents an abstract game, then we can analyze its strategic behavior in the
abstract game, and thus separate the cryptographic analysis of the protocol
from the strategic analysis
Unbounded violation of tripartite Bell inequalities
We prove that there are tripartite quantum states (constructed from random
unitaries) that can lead to arbitrarily large violations of Bell inequalities
for dichotomic observables. As a consequence these states can withstand an
arbitrary amount of white noise before they admit a description within a local
hidden variable model. This is in sharp contrast with the bipartite case, where
all violations are bounded by Grothendieck's constant. We will discuss the
possibility of determining the Hilbert space dimension from the obtained
violation and comment on implications for communication complexity theory.
Moreover, we show that the violation obtained from generalized GHZ states is
always bounded so that, in contrast to many other contexts, GHZ states do in
this case not lead to extremal quantum correlations. The results are based on
tools from the theories of operator spaces and tensor norms which we exploit to
prove the existence of bounded but not completely bounded trilinear forms from
commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more
accessible for a non-specialized reade
Why Philosophers Should Care About Computational Complexity
One might think that, once we know something is computable, how efficiently
it can be computed is a practical question with little further philosophical
importance. In this essay, I offer a detailed case that one would be wrong. In
particular, I argue that computational complexity theory---the field that
studies the resources (such as time, space, and randomness) needed to solve
computational problems---leads to new perspectives on the nature of
mathematical knowledge, the strong AI debate, computationalism, the problem of
logical omniscience, Hume's problem of induction, Goodman's grue riddle, the
foundations of quantum mechanics, economic rationality, closed timelike curves,
and several other topics of philosophical interest. I end by discussing aspects
of complexity theory itself that could benefit from philosophical analysis.Comment: 58 pages, to appear in "Computability: G\"odel, Turing, Church, and
beyond," MIT Press, 2012. Some minor clarifications and corrections; new
references adde
Probabilistic Operational Semantics for the Lambda Calculus
Probabilistic operational semantics for a nondeterministic extension of pure
lambda calculus is studied. In this semantics, a term evaluates to a (finite or
infinite) distribution of values. Small-step and big-step semantics are both
inductively and coinductively defined. Moreover, small-step and big-step
semantics are shown to produce identical outcomes, both in call-by- value and
in call-by-name. Plotkin's CPS translation is extended to accommodate the
choice operator and shown correct with respect to the operational semantics.
Finally, the expressive power of the obtained system is studied: the calculus
is shown to be sound and complete with respect to computable probability
distributions.Comment: 35 page
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