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Related papers: Quantum Merlin-Arthur and proofs without relative …

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We give a simpler proof of one of the results of Kobayashi, Le Gall, and Nishimura [arXiv:1210.1290v2], which shows that any QMA protocol can be converted to a one-sided error protocol, in which Arthur and Merlin initially share a constant…

Quantum Physics · Physics 2013-06-25 Attila Pereszlényi

Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…

Quantum Physics · Physics 2016-10-07 Thomas Vidick , John Watrous

Although it is believed unlikely that $\NP$-hard problems admit efficient quantum algorithms, it has been shown that a quantum verifier can solve $\NP$-complete problems given a "short" quantum proof; more precisely, $\NP\subseteq…

Quantum Physics · Physics 2011-06-22 Salman Beigi

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 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 construct a quantum oracle relative to which $\mathsf{BQP} = \mathsf{QMA}$ but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom…

Quantum Physics · Physics 2024-09-20 William Kretschmer

We propose a quantum authentication and digital signature protocol whose security is founded on the Quantum Merlin Arthur~(QMA)-completeness of the consistency of local density matrices. The protocol functions as a true public-key…

Quantum Physics · Physics 2025-06-23 Le-Ran Liu , Min-Quan He , Dan-Bo Zhang , Z. D. Wang

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 study the power of QMA(2) with postselection and show that the power is equal to NEXP. Our method for showing this equality can be also used to prove that other classes with exponentially small completeness-soundness gap equals to the…

Quantum Physics · Physics 2018-06-27 Yusuke Kinoshita

The class QMA plays a fundamental role in quantum complexity theory and it has found surprising connections to condensed matter physics and in particular in the study of the minimum energy of quantum systems. In this paper, we further…

Quantum Physics · Physics 2016-09-06 Alex B. Grilo , Iordanis Kerenidis , Jamie Sikora

We provide several advances to the understanding of the class of Quantum Merlin-Arthur proof systems (QMA), the quantum analogue of NP. Our central contribution is proving a longstanding conjecture that the Consistency of Local Density…

Quantum Physics · Physics 2022-10-13 Anne Broadbent , Alex B. Grilo

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

Given a verifier circuit for a problem in QMA, we show how to exponentially amplify the gap between its acceptance probabilities in the `yes' and `no' cases, with a method that is quadratically faster than the procedure given by Marriott…

Quantum Physics · Physics 2009-08-22 Daniel Nagaj , Pawel Wocjan , Yong Zhang

We present three contributions to the understanding of QMA with multiple provers: 1) We give a tight soundness analysis of the protocol of [Blier and Tapp, ICQNM '09], yielding a soundness gap Omega(1/N^2). Our improvement is achieved…

Quantum Physics · Physics 2013-02-01 Alessandro Chiesa , Michael A. Forbes

In this article we study the role that quantum resources play in quantum error correction assisted quantum metrology (QECQM) schemes. We show that there exist classes of such problems where entanglement is not necessary to retrieve noise…

Quantum Physics · Physics 2019-08-21 K. C. Tan , S. Omkar , H. Jeong

We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof…

Quantum Physics · Physics 2022-10-17 Marcel Dall'Agnol , Tom Gur , Subhayan Roy Moulik , Justin Thaler

This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA=QCMA. We prove three results about this question. First, we give a "quantum oracle separation" between QMA and QCMA. More…

Quantum Physics · Physics 2020-09-30 Scott Aaronson , Greg Kuperberg

Decision problems are the problems whose answer is either YES or NO. As the quantum analogue of $\mathsf{NP}$ (nondeterministic polynomial time), the class $\mathsf{QMA}$ (quantum Merlin-Arthur) contains the decision problems whose YES…

Quantum Physics · Physics 2020-10-08 Kai Sun , Zi-Jian Zhang , Fei Meng , Bin Cheng , Zhu Cao , Jin-Shi Xu , Man-Hong Yung , Chuan-Feng Li , Guang-Can Guo

Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA),…

Quantum Physics · Physics 2026-05-21 Zhaoyi Li , Elias Theil , Aram W. Harrow , Isaac Chuang

Quantum error correction assisted by entanglement helps to transmit the encoded qudits through quantum channels with some of them being noiseless. Here we consider a more realistic scheme for experiments what we called as partial-noisy…

Quantum Physics · Physics 2012-09-03 Zhuo Wang , Sixia Yu , Heng Fan , C. H. Oh