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Lower Bounds on the Communication Complexity of Binary Local Quantum Measurement Simulation

Adrian Kosowski 1, 2 Marcin Markiewicz 3 
1 CEPAGE - Algorithmics for computationally intensive applications over wide scale distributed platforms
Université Sciences et Technologies - Bordeaux 1, Inria Bordeaux - Sud-Ouest, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : We consider the problem of the classical simulation of quantum measurements in the scenario of communication complexity. Regev and Toner (2007) have presented a 2-bit protocol which simulates one particular correlation function arising from binary projective quantum measurements on arbitrary state, and in particular does not preserve local averages. The question of simulating other correlation functions using a protocol with bounded communication, or preserving local averages, has been posed as an open one. Within this paper we resolve it in the negative: we show that any such protocol must have unbounded communication for some subset of executions. In particular, we show that for any protocol, there exist inputs for which the random variable describing the number of communicated bits has arbitrarily large variance.
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Submitted on : Tuesday, October 8, 2013 - 6:35:16 PM
Last modification on : Saturday, June 25, 2022 - 8:29:48 PM
Long-term archiving on: : Thursday, January 9, 2014 - 4:35:17 AM


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  • HAL Id : hal-00871120, version 1
  • ARXIV : 1310.2217



Adrian Kosowski, Marcin Markiewicz. Lower Bounds on the Communication Complexity of Binary Local Quantum Measurement Simulation. 2013. ⟨hal-00871120⟩



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