Interaction in Quantum Communication and the Complexity of Set Disjointness

10/2001; DOI: 10.1145/380752.380786
Source: DBLP

ABSTRACT One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet in some scenarios there are ways of conveying information with much fewer, even exponentially fewer, qubits than possible classically [1], [2], [3]. Moreover, some of these methods have a very simple structure|they involve only few message exchanges between the communicating parties. We consider the question as to whether every classical protocol may be transformed to a simpler" quantum protocol|one that has similar eciency, but uses fewer message exchanges.

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    ABSTRACT: Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of quantum and classical channels and states. In this paper, we advocate a unified approach to an important class of problems in quantum Shannon theory, consisting of those that are bipartite, unidirectional, and memoryless.
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    ABSTRACT: This is an excerpt from my paper "On quantum and approximate privacy", published in Theory of Computing Systems vol.37(1), pp.221-246, 2004 (previous version in STACS 2002), and criticized by Jakoby et al. at this Dagstuhl workshop. Note that for the purpose of refuting Jacoby et al.'s claim that all functions can be computed privately in the quantum case it would suffice to consider the matrix for the two-bit Boolean AND in the proof of Theorem 2, for a more convenient argument. Moreover we sketch at the end how Jakoby et al.'s oblivious trans-fer protocol (starting on page 18 of the slides made available on this site, see the talk by Maciej Liskiewicz) fails against a simple EPR at-tack. Essentially their mistake is to ignore Alice's ability to keep a purification of her "random bits" instead of simply tossing coins, an attack that is undetectable for Bob and hence allowed in our definition of privacy.

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May 20, 2014