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Complexity measures and decision tree complexity: a survey
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Quantum lower bounds by polynomials
TLDR
This work examines the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}/sup N/ in the black-box model and gives asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings.
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Quantum vs. classical communication and computation
TLDR
A simple and general simulation technique is presented that transforms any black-box quantum algorithm to a quantum communication protocol for a related problem, in a way that fully exploits the quantum parallelism, to obtain new positive and negative results.
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Quantum fingerprinting.
TLDR
It is shown that fingerprints consisting of quantum information can be made exponentially smaller than the original strings without any correlations or entanglement between the parties, implying an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity.
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SUBSTITUTING QUANTUM ENTANGLEMENT FOR COMMUNICATION
We show that quantum entanglement can be used as a substitute for communication when the goal is to compute a function whose input data are distributed among remote parties. Specifically, we show…
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Are bitvectors optimal?
TLDR
Deterministic schemes for the static membership problem are considered and tradeoffs between space and the number of probes are shown.
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Quantum verification of matrix products
TLDR
A quantum algorithm that verifies a product of two n × n matrices over any integral domain with bounded error in worst-case time O(n) and expected time ω, where ω is the number of wrong entries is presented.
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On Computation and Communication with Small Bias
  • H. Buhrman
  • Computer Science, Mathematics
    Twenty-Second Annual IEEE Conference on…
  • 13 June 2007
TLDR
This work combines a query complexity separation due to Beigel with a technique of Razborov that translates the acceptance probability of quantum protocols to polynomials and study how small the bias of minimal-degree polynmials that sign-represent Boolean functions needs to be.
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Optimal resiliency against mobile faults
TLDR
A protocol for MF(/sup 1///sub 3/,1), which is optimal for this family of mobile fault models, and the running time of the protocol is O(n) rounds, also optimal for these models.
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Position-Based Quantum Cryptography: Impossibility and Constructions
TLDR
It is proved that with the help of sufficient pre-shared entanglement, any non-local quantum computation, i.e., any computation that involves quantum inputs from two parties at different locations, can be performed instantaneously and without any communication, up to local corrections that need to be applied to the outputs.
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