TY - JOUR
T1 - The quantum communication complexity of sampling
AU - Ambainis, Andris
AU - Schulman, Leonard J.
AU - Ta-Shma, Amnon
AU - Vazirani, Umesh
AU - Wigderson, Avi
PY - 2003/9
Y1 - 2003/9
N2 - Sampling is an important primitive in probabilistic and quantum algorithms. In the spirit of communication complexity, given a function f: X×Y→{0, 1} and a probability distribution D over X×Y, we define the sampling complexity of (f, D] as the minimum number of bits that Alice and Bob must communicate for Alice to pick x∈X and Bob to pick y∈Y as well as a value z such that the resulting distribution of (x, y, z) is close to the distribution (D, f(D)). In this paper we initiate the study of sampling complexity, in both the classical and quantum models. We give several variants of a definition. We completely characterize some of these variants and give upper and lower bounds on others. In particular, this allows us to establish an exponential gap between quantum and classical sampling complexity for the set-disjointness function.
AB - Sampling is an important primitive in probabilistic and quantum algorithms. In the spirit of communication complexity, given a function f: X×Y→{0, 1} and a probability distribution D over X×Y, we define the sampling complexity of (f, D] as the minimum number of bits that Alice and Bob must communicate for Alice to pick x∈X and Bob to pick y∈Y as well as a value z such that the resulting distribution of (x, y, z) is close to the distribution (D, f(D)). In this paper we initiate the study of sampling complexity, in both the classical and quantum models. We give several variants of a definition. We completely characterize some of these variants and give upper and lower bounds on others. In particular, this allows us to establish an exponential gap between quantum and classical sampling complexity for the set-disjointness function.
KW - Communication complexity
KW - Quantum communication complexity
KW - Quantum information theory
KW - Set-disjointness
KW - The log-rank conjecture in communication complexity
UR - http://www.scopus.com/inward/record.url?scp=0942299111&partnerID=8YFLogxK
U2 - 10.1137/S009753979935476
DO - 10.1137/S009753979935476
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AN - SCOPUS:0942299111
SN - 0097-5397
VL - 32
SP - 1570
EP - 1585
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
IS - 6
ER -