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Related papers: Quantum Arthur-Merlin Games

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This paper introduces quantum ``multiple-Merlin''-Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multi-proof systems are obviously equivalent to classical…

Quantum Physics · Physics 2008-05-12 Hirotada Kobayashi , Keiji Matsumoto , Tomoyuki Yamakami

This paper investigates the role of interaction and coins in public-coin quantum interactive proof systems (also called quantum Arthur-Merlin games). While prior works focused on classical public coins even in the quantum setting, the…

Quantum Physics · Physics 2019-05-23 Hirotada Kobayashi , François Le Gall , Harumichi Nishimura

QMA (Quantum Merlin Arthur) is the class of problems which, though potentially hard to solve, have a quantum solution which can be verified efficiently using a quantum computer. It thus forms a natural quantum version of the classical…

Quantum Physics · Physics 2016-03-02 Tomoyuki Morimae , Daniel Nagaj , Norbert Schuch

What happens if in QMA the quantum channel between Merlin and Arthur is noisy? It is not difficult to show that such a modification does not change the computational power as long as the noise is not too strong so that errors are…

Quantum Physics · Physics 2016-08-18 Tomoyuki Morimae , Keisuke Fujii , Harumichi Nishimura

We show that the class QMA does not change even if we restrict Arthur's computing ability to only Clifford gate operations (plus classical XOR gate). The idea is to use the fact that the preparation of certain single-qubit states, so called…

Quantum Physics · Physics 2015-09-25 Tomoyuki Morimae , Masahito Hayashi , Harumichi Nishimura , Keisuke Fujii

We introduce and study a new model of interactive proofs: AM(k), or Arthur-Merlin with k non-communicating Merlins. Unlike with the better-known MIP, here the assumption is that each Merlin receives an independent random challenge from…

Computational Complexity · Computer Science 2014-01-28 Scott Aaronson , Russell Impagliazzo , Dana Moshkovitz

The complexity of free games with two or more classical players was essentially settled by Aaronson, Impagliazzo, and Moshkovitz (CCC'14). There are two complexity classes that can be considered quantum analogues of classical free games:…

Quantum Physics · Physics 2023-02-10 Anand Natarajan , Tina Zhang

We study a generalization of the Mermin-Peres magic square game to arbitrary rectangular dimensions. After exhibiting some general properties, these rectangular games are fully characterized in terms of their optimal win probabilities for…

Quantum Physics · Physics 2020-12-11 Sean A. Adamson , Petros Wallden

In classical Arthur-Merlin games, the class of languages whose membership proofs can be verified by Arthur using logarithmic space (AM(log-space)) coincides with the class P \cite{Co89}. In this note, we show that if Arthur has a fixed-size…

Computational Complexity · Computer Science 2012-04-06 Abuzer Yakaryilmaz , A. C. Cem Say

Quantum Merlin-Arthur proof systems are believed to be stronger than both their classical counterparts and ``stand-alone'' quantum computers when Arthur is assumed to operate in $\Omega(\log n)$ space. No hint of such an advantage over…

Computational Complexity · Computer Science 2025-05-14 A. C. Cem Say

We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state psi whose maximum overlap with a product state is 1-epsilon, the test passes with…

Quantum Physics · Physics 2013-10-03 Aram W. Harrow , Ashley Montanaro

This paper presents stronger methods of achieving perfect completeness in quantum interactive proofs. First, it is proved that any problem in QMA has a two-message quantum interactive proof system of perfect completeness with constant…

Quantum Physics · Physics 2016-05-25 Hirotada Kobayashi , François Le Gall , Harumichi Nishimura

We show how to encode $2^n$ (classical) bits $a_1,...,a_{2^n}$ by a single quantum state $|\Psi>$ of size O(n) qubits, such that: for any constant $k$ and any $i_1,...,i_k \in \{1,...,2^n\}$, the values of the bits $a_{i_1},...,a_{i_k}$ can…

Quantum Physics · Physics 2007-05-23 Ran Raz

This paper gives a QMA (Quantum Merlin-Arthur) protocol for 3-SAT with two logarithmic-size quantum proofs (that are not entangled with each other) such that the gap between the completeness and the soundness is Omega(1/n polylog(n)). This…

Quantum Physics · Physics 2021-10-05 Francois Le Gall , Shota Nakagawa , Harumichi Nishimura

This paper proves one of the open problem posed by Beigi et al. in arXiv:1004.0411v2. We consider quantum interactive proof systems where in the beginning the verifier and prover send messages to each other with the combined length of all…

Computational Complexity · Computer Science 2011-09-06 Attila Pereszlényi

We show several results related to interactive proof modes of communication complexity. First we show lower bounds for the QMA-communication complexity of the functions Inner Product and Disjointness. We describe a general method to prove…

Computational Complexity · Computer Science 2011-01-04 Hartmut Klauck

The Mermin-Peres magic square game is a cooperative two-player nonlocal game in which shared quantum entanglement allows the players to win with certainty, while players limited to classical operations cannot do so, a phenomenon dubbed…

Quantum Physics · Physics 2012-09-19 Alex Arkhipov

In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…

Quantum Physics · Physics 2024-03-21 Anand Natarajan , Chinmay Nirkhe

We show that given an explicit description of a multiplayer game, with a classical verifier and a constant number of players, it is QMA-hard, under randomized reductions, to distinguish between the cases when the players have a strategy…

Quantum Physics · Physics 2019-02-12 Anand Natarajan , Thomas Vidick

Let L be a language decided by a constant-round quantum Arthur-Merlin (QAM) protocol with negligible soundness error and all but possibly the last message being classical. We prove that if this protocol is zero knowledge with a black-box,…

Quantum Physics · Physics 2009-06-19 Rahul Jain , Alexandra Kolla , Gatis Midrijanis , Ben W. Reichardt
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