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Given one or more uses of a classical channel, only a certain number of messages can be transmitted with zero probability of error. The study of this number and its asymptotic behavior constitutes the field of classical zero-error information theory. We show that, given a single use of certain classical channels, entangled states of a system shared by the(More)
We consider the problem of efficiently enumerating the satisfying assignments to AC 0 circuits. We give a zero-error randomized algorithm which takes an AC 0 circuit as input and constructs a set of restrictions which partition {0, 1} n so that under each restriction the value of the circuit is constant. Let d denote the depth of the circuit and cn denote(More)
We present two new approximation algorithms for Unique Games. The first generalizes the results of [2, 15] who give polynomial time approximation algorithms for graphs with high conductance. We give a polynomial time algorithm assuming only good local conductance, i.e. high conductance for small subgraphs. The second algorithm runs in mildly exponential(More)
BACKGROUND Hematopoiesis entails the production of multiple blood cell lineages throughout the lifespan of the organism. This is accomplished by the regulated expansion and differentiation of hematopoietic precursors that originate from self-renewing hematopoietic stem cells. Studies of lineage commitment and proliferation have shown that the cytokine(More)
We derive upper bounds on the rate of transmission of classical information over quantum channels by block codes with a given blocklength and error probability, for both entanglement-assisted and unassisted codes, in terms of a unifying framework of quantum hypothesis testing with restricted measurements. Our bounds do not depend on any special property of(More)
—Shannon's theory of zero-error communication is reexamined in the broader setting of using one classical channel to simulate another exactly, and in the presence of various resources that are all classes of non-signalling correlations: Shared randomness, shared entanglement and arbitrary non-signalling correlations. Specifically, when the channel being(More)
We derive one-shot upper bounds for quantum noisy channel codes. We do so by regarding a channel code as a bipartite operation with an encoder belonging to the sender and a decoder belonging to the receiver, and imposing constraints on the bipartite operation. We investigate the power of codes whose bipartite operation is non-signalling from Alice to Bob,(More)
The capability of a given channel to transmit information is, a priori, distinct from its capability to distribute random correlations. Despite that, for classical channels, the capacity to distribute information and randomness turns out to be the same, even with the assistance of auxiliary communication. In this work we show that this is no longer true for(More)