Dave Touchette

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Coding theorems in quantum Shannon theory express the ultimate rates at which a sender can transmit information over a noisy quantum channel. More often than not, the known formulas expressing these transmission rates are intractable, requiring an optimization over an infinite number of uses of the channel. Researchers have rarely found quantum channels(More)
In quantum state redistribution as introduced by Luo and Devetak and Devetak and Yard, there are four systems of interest: the A system held by Alice; the B system held by Bob; the C system that is to be transmitted from Alice to Bob; and the R system that holds a purification of the state in the ABC registers. We give upper and lower bounds on the amount(More)
We define a new notion of information cost for quantum protocols, and a corresponding notion of quantum information complexity for bipartite quantum tasks. These are the fully quantum generalizations of the analogous quantities for bipartite classical tasks that have found many applications recently, in particular for proving communication complexity lower(More)
We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with r rounds, we prove a lower bound of Omega(n/r) on the communication required for computing disjointness of input size n, which is optimal up to logarithmic factors. The previous best lower bound was(More)
We study the problem of simulating protocols in a quantum communication setting over noisy channels. This problem falls at the intersection of quantum information theory and quantum communication complexity, and will be of importance for eventual real-world applications of interactive quantum protocols, which can be proved to have exponentially lower(More)
We present the first general direct sum theorem for quantum communication complexity that holds for more than a single round of communication. A direct sum theorem states that to compute n tasks simultaneously requires as much resources as the amount of the given resource required for computing them separately. By a general direct sum theorem, we mean a(More)
In the context of two-party interactive quantum communication protocols, we study a recently defined notion of quantum information cost (QIC), which possesses most of the important properties of its classical analogue, see Ref. [Tou15]. Notably, its link with amortized quantum communication complexity has been used in Ref. [BGKK + 15] to prove an (almost)(More)
We exhibit a Boolean function for which the quantum communication complexity is exponentially larger than the classical information complexity. An exponential separation in the other direction was already known from the work of Kerenidis et. al. [SICOMP 44, pp. 1550–1572], hence our work implies that these two complexity measures are incomparable. As(More)