Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Sampling is an important primitive in probabilistic and quantum algorithms. In the spirit of communication complexity, given a function f: X/spl times/Y/spl rarr/{0,1} and a probability distribution D over X/spl times/Y,  define the sampling complexity of (f,D) as the minimum number of bits Alice and Bob must communicate for Alice to pick x/spl isin/X and Bob to pick y/spl isin/Y as ll as a valve z s.t. the resulting distribution of (x,y,z) is close to the distribution (D,f(D)).   initiate the study of sampling complexity, in both the classical and quantum model.  give several variants of the definition.  completely characterize some of these tasks, and give upper and lor bounds on others. In particular this allows us to establish an exponential gap beten quantum and classical sampling complexity, for the set disjointness function. This is the first exponential gap for any task where the classical probabilistic algorithm is allod to err.
['Andris Ambainis', 'Leonard J. Schulman', 'Amnon Ta-Shma', 'Umesh V. Vazirani', 'Avi Wigderson']
I am writing a research paper on a idea The quantum communication complexity of sampling
[{"from": "human", "value": "I am writing a research paper on a idea The quantum communication complexity of sampling"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Sampling is an important primitive in probabilistic and quantum algorithms. In the spirit of communication complexity, given a function f: X/spl times/Y/spl rarr/{0,1} and a probability distribution D over X/spl times/Y,  define the sampling complexity of (f,D) as the minimum number of bits Alice and Bob must communicate for Alice to pick x/spl isin/X and Bob to pick y/spl isin/Y as ll as a valve z s.t. the resulting distribution of (x,y,z) is close to the distribution (D,f(D)).   initiate the study of sampling complexity, in both the classical and quantum model.  give several variants of the definition.  completely characterize some of these tasks, and give upper and lor bounds on others. In particular this allows us to establish an exponential gap beten quantum and classical sampling complexity, for the set disjointness function. This is the first exponential gap for any task where the classical probabilistic algorithm is allod to err."}]