QMA(2) with Limited Shared Entanglement
Abstract
In QMA(2), two computationally unbounded provers submit unentangled quantum witnesses to a polynomial-time quantum verifier. We ask whether allowing limited shared entanglement between the two provers changes the power of QMA(2). To this end, we formalize QMA(2;h), a variant in which the provers initially share h EPR pairs, as suggested by Aaronson, Beigi, Drucker, Fefferman, and Shor (ToC~2009). We show that polynomially many shared EPR pairs give the provers no cheating advantage: QMA(2)⊆QMA(2;h) for h=poly(n). For logarithmically many pairs, the power of QMA(2) remains unchanged, strengthening this inclusion to QMA(2)=QMA(2;h) for h=O(log n). Finally, we introduce a variant that also allows classical communication between the provers when preparing the witnesses. This setting is particularly revealing for logarithmic-size witnesses: assuming NPnsubseteqBQP, we show that superlogarithmically many shared EPR pairs strictly reduce the model's computational power.
Related
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BibTeX
@misc{schiava2026qma2,
title = {{QMA(2) with Limited Shared Entanglement}},
author = {Alex Della Schiava and Ranitha Mataraarachchi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39668},
eprint = {2609.39668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39668},
}
RIS
TY - UNPB
TI - QMA(2) with Limited Shared Entanglement
AU - Alex Della Schiava
AU - Ranitha Mataraarachchi
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2609.39668
UR - https://arxiv.org/abs/2609.39668
AB - In QMA(2), two computationally unbounded provers submit unentangled quantum witnesses to a polynomial-time quantum verifier. We ask whether allowing limited shared entanglement between the two provers changes the power of QMA(2). To this end, we formalize QMA(2;h), a variant in which the provers initially share h EPR pairs, as suggested by Aaronson, Beigi, Drucker, Fefferman, and Shor (ToC~2009). We show that polynomially many shared EPR pairs give the provers no cheating advantage: QMA(2)⊆QMA(2;h) for h=poly(n). For logarithmically many pairs, the power of QMA(2) remains unchanged, strengthening this inclusion to QMA(2)=QMA(2;h) for h=O(log n). Finally, we introduce a variant that also allows classical communication between the provers when preparing the witnesses. This setting is particularly revealing for logarithmic-size witnesses: assuming NPnsubseteqBQP, we show that superlogarithmically many shared EPR pairs strictly reduce the model's computational power.
ER -