TY - JOUR

T1 - Interaction in quantum communication and the complexity of set disjointness

AU - Klauck, H.

AU - Nayak, A.

AU - Ta-Shma, A.

AU - Zuckerman, D.

PY - 2001

Y1 - 2001

N2 - 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 exponentially fewer qubits than possible classically. Moreover, 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 efficiency, but uses fewer message exchanges. We show that for any constant k, there is a problem such that its k + 1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity, thus answering the above question in the negative. This in particular proves a round hierarchy theorem for quantum communication complexity, and implies via a simple reduction, an Ω(N1/k) lower bound for k message protocols for Set Disjointness for constant k. Our result builds on two primitives, local transitions in bipartite states (based on previous work) and average encoding which may be of significance in other contexts as well.

AB - 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 exponentially fewer qubits than possible classically. Moreover, 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 efficiency, but uses fewer message exchanges. We show that for any constant k, there is a problem such that its k + 1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity, thus answering the above question in the negative. This in particular proves a round hierarchy theorem for quantum communication complexity, and implies via a simple reduction, an Ω(N1/k) lower bound for k message protocols for Set Disjointness for constant k. Our result builds on two primitives, local transitions in bipartite states (based on previous work) and average encoding which may be of significance in other contexts as well.

UR - http://www.scopus.com/inward/record.url?scp=0034819349&partnerID=8YFLogxK

U2 - 10.1145/380752.380786

DO - 10.1145/380752.380786

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AN - SCOPUS:0034819349

SN - 0734-9025

SP - 124

EP - 133

JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

T2 - 33rd Annual ACM Symposium on Theory of Computing

Y2 - 6 July 2001 through 8 July 2001

ER -