536 research outputs found
A parallel repetition theorem for all entangled games
The behavior of games repeated in parallel, when played with quantumly
entangled players, has received much attention in recent years. Quantum
analogues of Raz's classical parallel repetition theorem have been proved for
many special classes of games. However, for general entangled games no parallel
repetition theorem was known. We prove that the entangled value of a two-player
game repeated times in parallel is at most for a
constant depending on , provided that the entangled value of is
less than 1. In particular, this gives the first proof that the entangled value
of a parallel repeated game must converge to 0 for all games whose entangled
value is less than 1. Central to our proof is a combination of both classical
and quantum correlated sampling.Comment: To appear in the 43rd International Colloquium on Automata,
Languages, and Programming (ICALP
New security notions and feasibility results for authentication of quantum data
We give a new class of security definitions for authentication in the quantum
setting. These definitions capture and strengthen existing definitions of
security against quantum adversaries for both classical message authentication
codes (MACs) and well as full quantum state authentication schemes. The main
feature of our definitions is that they precisely characterize the effective
behavior of any adversary when the authentication protocol accepts, including
correlations with the key. Our definitions readily yield a host of desirable
properties and interesting consequences; for example, our security definition
for full quantum state authentication implies that the entire secret key can be
re-used if the authentication protocol succeeds.
Next, we present several protocols satisfying our security definitions. We
show that the classical Wegman-Carter authentication scheme with 3-universal
hashing is secure against superposition attacks, as well as adversaries with
quantum side information. We then present conceptually simple constructions of
full quantum state authentication.
Finally, we prove a lifting theorem which shows that, as long as a protocol
can securely authenticate the maximally entangled state, it can securely
authenticate any state, even those that are entangled with the adversary. Thus,
this shows that protocols satisfying a fairly weak form of authentication
security automatically satisfy a stronger notion of security (in particular,
the definition of Dupuis, et al (2012)).Comment: 50 pages, QCrypt 2016 - 6th International Conference on Quantum
Cryptography, added a new lifting theorem that shows equivalence between a
weak form of authentication security and a stronger notion that considers
side informatio
Finite-amplitude interfacial waves in the presence of a current
Solutions for interfacial waves of permanent form in the presence of a current wcre obtained for small-to-moderate wave amplitudes. A weakly nonlinear approximation was used to give simple analytical solutions to second order in wave height. Numerical methods were usctl to obtain solutions for larger wave amplitudes, details are reported for a number of selected cases. A special class of finite-amplitude solutions, closely related to the well-known Stokes surface waves, were identified. Factors limiting the existence of steady solutions are examined
A No-Go Theorem for Derandomized Parallel Repetition: Beyond Feige-Kilian
In this work we show a barrier towards proving a randomness-efficient
parallel repetition, a promising avenue for achieving many tight
inapproximability results. Feige and Kilian (STOC'95) proved an impossibility
result for randomness-efficient parallel repetition for two prover games with
small degree, i.e., when each prover has only few possibilities for the
question of the other prover. In recent years, there have been indications that
randomness-efficient parallel repetition (also called derandomized parallel
repetition) might be possible for games with large degree, circumventing the
impossibility result of Feige and Kilian. In particular, Dinur and Meir
(CCC'11) construct games with large degree whose repetition can be derandomized
using a theorem of Impagliazzo, Kabanets and Wigderson (SICOMP'12). However,
obtaining derandomized parallel repetition theorems that would yield optimal
inapproximability results has remained elusive.
This paper presents an explanation for the current impasse in progress, by
proving a limitation on derandomized parallel repetition. We formalize two
properties which we call "fortification-friendliness" and "yields robust
embeddings." We show that any proof of derandomized parallel repetition
achieving almost-linear blow-up cannot both (a) be fortification-friendly and
(b) yield robust embeddings. Unlike Feige and Kilian, we do not require the
small degree assumption.
Given that virtually all existing proofs of parallel repetition, including
the derandomized parallel repetition result of Dinur and Meir, share these two
properties, our no-go theorem highlights a major barrier to achieving
almost-linear derandomized parallel repetition
A note on numerical computations of large amplitude standing waves
Numerical solutions of the inviscid equations that describe standing waves of finite amplitude on deep water are reported. The calculations suggest that standing waves exist of steepness, height and energy greater than the limiting wave of Penney & Price (1952). The computed profiles are found to be consistent with Taylor's (1953) experimental observations
A new type of three-dimensional deep-water wave of permanent form
A new class of three-dimensional, deep-water gravity waves of permanent form has been found using an equation valid for weakly nonlinear waves due to Zakharov (1968). These solutions appear as bifurcations from the uniform two-dimensional wave train. The critical wave heights are given as functions of the modulation wave vector. The three-dimensional patterns may be skewed or symmetrical. An example of the skewed wave pattern is given and shown to be stable. The results become exact in the limit of very oblique modulations
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