
Lower Bounds for XOR of Forrelations
The Forrelation problem, introduced by Aaronson [A10] and Aaronson and A...
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Exponential Separation between Quantum Communication and Logarithm of Approximate Rank
Chattopadhyay, Mande and Sherif (ECCC 2018) recently exhibited a total B...
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Quantum Communication Complexity of Distribution Testing
The classical communication complexity of testing closeness of discrete ...
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Communication Complexity of Private Simultaneous Quantum Messages Protocols
The private simultaneous messages model is a noninteractive version of ...
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Postselected Classical Query Complexity
We study classical query algorithms with postselection, and find that t...
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On the Exponential Sample Complexity of the Quantum State Sign Estimation Problem
We demonstrate that the ability to estimate the relative sign of an arbi...
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Exponential quantum communication reductions from generalizations of the Boolean Hidden Matching problem
In this work we revisit the Boolean Hidden Matching communication problem, which was the first communication problem in the oneway model to demonstrate an exponential classicalquantum communication separation. In this problem, Alice's bits are matched into pairs according to a partition that Bob holds. These pairs are compressed using a Parity function and it is promised that the final bitstring is equal either to another bitstring Bob holds, or its complement. The problem is to decide which case is the correct one. Here we generalize the Boolean Hidden Matching problem by replacing the parity function with an arbitrary function f. Efficient communication protocols are presented depending on the signdegree of f. If its signdegree is less than or equal to 1, we show an efficient classical protocol. If its signdegree is less than or equal to 2, we show an efficient quantum protocol. We then completely characterize the classical hardness of all symmetric functions f of signdegree greater than or equal to 2, except for one family of specific cases. We also prove, via Fourier analysis, a classical lower bound for any function f whose pure high degree is greater than or equal to 2. Similarly, we prove, also via Fourier analysis, a quantum lower bound for any function f whose pure high degree is greater than or equal to 3. These results give a large family of new exponential classicalquantum communication separations.
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