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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)
The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly so that they can be decoded with zero probability of error. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the(More)
The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more physically meaningful is to restrict the Hamiltonian in question by picking its terms from a fixed set S. Examples of such(More)
Suppose that Alice and Bob receive a pair (x, u) with probability Q(x, u). Alice wishes to send x to Bob, using a noisy classical channel N , such that Bob can determine x with zero chance of error. Without making use of entanglement, this is known [2] to be possible iff there is a graph homomorphism G → H between the graphs x ∼ G y ⇐⇒ ∃u ∈ U such that Q(x,(More)
Spin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. Here, we prove that all the physics of every classical spin model is reproduced in the low-energy sector of certain "universal models," with at most polynomial overhead. This holds for classical models with discrete or(More)
We show that deciding whether a given quantum channel can be generated by a Markovian master equation is an NP-hard problem. As a consequence , this result suggests that extracting the underlying physics governing the evolution of a quantum system, as described by its dynamical equations, may be a hard task regardless of how much data is gathered via(More)
The theory of zero-error communication is re-examined in the broader setting of using one classical channel to simulate another exactly in the presence of various classes of nonsignalling correlations between sender and receiver i.e., shared randomness, shared entanglement and arbitrary nonsignalling correlations. When the channel being simulated is(More)
The zero-error capacity of a channel is the rate at which it can send information perfectly, with zero probability of error, and has long been studied in classical information theory. We show that the zero-error capacity of quantum channels exhibits an extreme form of nonadditivity, one which is not possible for classical channels, or even for the usual(More)