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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 in [Luo and Devetak (2009)] and [Devetak and Yard (2008)], 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… (More)

We define a new notion of information cost for quantum protocols, and a corresponding notion of quantum information complexity for bipartite quantum channels, and then investigate the properties of such quantities. These are the fully quantum generalizations of the analogous quantities for bipartite classical functions that have found many applications… (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 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 is of particular importance for real-world applications of interactive quantum protocols, which can be proved to have exponentially 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˜Ω(n/r + 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 Ω(n/r 2 + r) due to… (More)

We prove a direct sum theorem for bounded round entanglement-assisted quantum communication complexity. To do so, we use the fully quantum definition for information cost and complexity that we recently introduced, and use both the fact that information is a lower bound on communication, and the fact that a direct sum property holds for quantum information… (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)

We prove a lower bound on the information leakage of any classical protocol computing the equality function in the simultaneous message passing (SMP) model. Our bound is valid in the finite length regime and is strong enough to demonstrate a quantum advantage in terms of information leakage for practical quantum protocols. We prove our bound by obtaining an… (More)

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