Gharibian, Sevag
Sevag
Gharibian0000-0002-9992-3379
Sikora, Jamie
Jamie
Sikora
Upadhyay, Sarvagya
Sarvagya
Upadhyay
QMA variants with polynomially many provers
2013
2019-03-01T12:00:39Z
2019-03-06T22:00:06Z
journal_article
https://ris.uni-paderborn.de/record/8173
https://ris.uni-paderborn.de/record/8173.json
1108.0617
We study three variants of multi-prover quantum Merlin-Arthur proof systems. We first show that the class of problems that can be efficiently verified using polynomially many quantum proofs, each of logarithmic-size, is exactly MQA (also known as QCMA), the class of problems which can be efficiently verified via a classical proof and a quantum verifier. We then study the class BellQMA(poly), characterized by a verifier who first applies unentangled, nonadaptive measurements to each of the polynomially many proofs, followed by an arbitrary but efficient quantum verification circuit on the resulting measurement outcomes. We show that if the number of outcomes per nonadaptive measurement is a polynomially-bounded function, then the expressive power of the proof system is exactly QMA. Finally, we study a class equivalent to QMA(m), denoted SepQMA(m), where the verifier's measurement operator corresponding to outcome "accept" is a fully separable operator across the m quantum proofs. Using cone programming duality, we give an alternate proof of a result of Harrow and Montanaro [FOCS, pp. 633--642 (2010)] that shows a perfect parallel repetition theorem for SepQMA(m) for any m.