相关论文: Quantum Arthur-Merlin Games

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…

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…

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…

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…

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…

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…

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:…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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,…