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We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with oracle access to their inputs.
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Dmitry Gavinsky, Julia Kempe, Iordanis Kerenidis, Ran Raz, Ronald de Wolf: Exponential Separation for One-Way Quantum Communication Complexity, with Applications to Cryptography. SIAM J. Comput. 38(5): 1695-1708 (2008)
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Eshan Chattopadhyay, Pooya Hatami, Kaave Hosseini, Shachar Lovett: Pseudorandom Generators from Polarizing Random Walks. CCC 2018: 1:1-1:21
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Hamed Hatami, Kaave Hosseini, Shachar Lovett: Structure of Protocols for XOR Functions. SIAM J. Comput. 47(1): 208-217 (2018)
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Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, Toniann Pitassi: Query-To-Communication Lifting for BPP Using Inner Product. ICALP 2019: 35:1-35:15
2019
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Eshan Chattopadhyay, Pooya Hatami, Shachar Lovett, Avishay Tal: Pseudorandom Generators from the Second Fourier Level and Applications to AC0 with Parity Gates. ITCS 2019: 22:1-22:15
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Dmitry Gavinsky: Entangled simultaneity versus classical interactivity in communication complexity. STOC 2016: 877-884
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Christopher Musco: Lecture Notes in Advanced Algorithm Design: Concentration Bounds, Available at https://www.cs.princeton.edu/courses/archive/fall18/cos521/Lectures/lec3.pdf
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Chebyshev’s Inequality - Wikipedia
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Bernstein Inequalities - Wikipedia
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Ran Raz and Avishay Tal: Oracle separation of BQP and PH. STOC 2019: 13-23
2019
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