120 research outputs found
A Family of Indecomposable Positive Linear Maps based on Entangled Quantum States
We introduce a new family of indecomposable positive linear maps based on
entangled quantum states. Central to our construction is the notion of an
unextendible product basis. The construction lets us create indecomposable
positive linear maps in matrix algebras of arbitrary high dimension.Comment: 16 pages LaTex: updated and a derivation of a lower bound on epsilon
is added and calculated for one of the examples. Submitted to Lin. Alg. and
Its App
The Bounded Storage Model in The Presence of a Quantum Adversary
An extractor is a function E that is used to extract randomness. Given an
imperfect random source X and a uniform seed Y, the output E(X,Y) is close to
uniform. We study properties of such functions in the presence of prior quantum
information about X, with a particular focus on cryptographic applications. We
prove that certain extractors are suitable for key expansion in the bounded
storage model where the adversary has a limited amount of quantum memory. For
extractors with one-bit output we show that the extracted bit is essentially
equally secure as in the case where the adversary has classical resources. We
prove the security of certain constructions that output multiple bits in the
bounded storage model.Comment: 13 pages Latex, v3: discussion of independent randomizers adde
Constructions and Noise Threshold of Hyperbolic Surface Codes
We show how to obtain concrete constructions of homological quantum codes
based on tilings of 2D surfaces with constant negative curvature (hyperbolic
surfaces). This construction results in two-dimensional quantum codes whose
tradeoff of encoding rate versus protection is more favorable than for the
surface code. These surface codes would require variable length connections
between qubits, as determined by the hyperbolic geometry. We provide numerical
estimates of the value of the noise threshold and logical error probability of
these codes against independent X or Z noise, assuming noise-free error
correction
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