arXiv subjects

H. Buhrman

Publications and source records attributed to H. Buhrman.

4 recordsLinked to original sources

arXiv2005

Causality and Cirel'son bounds

An EPR-Bell type experiment carried out on an entangled quantum system can produce correlations stronger than allowed by local realistic theories. However there are correlations that are no-signaling and are more non local than the quantum correlations. Here we show that any correlations more non local than those achievable in an EPR-Bell type experiment necessarily allow -in the context of the quantum formalism- both for signaling and for generation of entanglement. We use our approach to rederive Cirel'son bound for the CHSH expression, and we derive a new Cirel'son type bound for qutrits. We discuss in detail the interpretation of our approach.

quant-ph↗

arXiv2004

Multipartite Nonlocal Quantum Correlations Resistant to Imperfections

We use techniques for lower bounds on communication to derive necessary conditions in terms of detector efficiency or amount of super-luminal communication for being able to reproduce with classical local hidden-variable theories the quantum correlations occurring in EPR-type experiments in the presence of noise. We apply our method to an example involving n parties sharing a GHZ-type state on which they carry out measurements and show that for local-hidden variable theories, the amount of super-luminal classical communication c and the detector efficiency eta are constrained by eta 2^(-c/n) = O(n^(-1/6)) even for constant general error probability epsilon = O(1).

quant-ph↗

arXiv2002

Quantum Property Testing

A language L has a property tester if there exists a probabilistic algorithm that given an input x only asks a small number of bits of x and distinguishes the cases as to whether x is in L and x has large Hamming distance from all y in L. We define a similar notion of quantum property testing and show that there exist languages with quantum property testers but no good classical testers. We also show there exist languages which require a large number of queries even for quantumly testing.

quant-ph↗

arXiv1999

Bounds for Small-Error and Zero-Error Quantum Algorithms

We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search algorithms, their error probability, the size of the search space, and the number of solutions in this space. Using this, we deduce new lower and upper bounds for quantum versions of amplification problems. Next, we establish nearly optimal quantum-classical separations for the query complexity of monotone functions in the zero-error model (where our quantum zero-error model is defined so as to be robust when the quantum gates are noisy). Also, we present a communication complexity problem related to a total function for which there is a quantum-classical communication complexity gap in the zero-error model. Finally, we prove separations for monotone graph properties in the zero-error and other error models which imply that the evasiveness conjecture for such properties does not hold for quantum computers.

cs.CC↗