Related papers: Quantum Merlin-Arthur Proof Systems: Are Multiple …

The central question in quantum multi-prover interactive proof systems is whether or not entanglement shared between provers affects the verification power of the proof system. We study for the first time positive aspects of prior…

Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…

In this paper, we introduce a new public quantum interactive proof system and the first quantum alternating Turing machine: qAM proof system and qATM, respectively. Both are obtained from their classical counterparts (Arthur-Merlin proof…

We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and…

In this paper we explore the power of AM for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA)--introduced by Ambainis and Watrous in 2002--and the communications are classical. It is of…

Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…

We introduce Merlin-Arthur (MA) automata where Merlin provides a certificate at the beginning of computation and it is scanned by Arthur before reading the input. We define Merlin-Arthur deterministic, probabilistic, and quantum finite…

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…

We show that any number of parties can coherently exchange any one pure quantum state for another, without communication, given prior shared entanglement. Two applications of this fact to the study of multi-prover quantum interactive proof…

In this note we study the power of so called query-limited computers. We compare the strength of a classical computer that is allowed to ask two questions to an NP-oracle with the strength of a quantum computer that is allowed only one such…

The way entanglement influences the power of quantum and classical multi-prover interactive proof systems is a long-standing open question. We show that the class of languages recognized by quantum multi-prover interactive proof systems,…

We construct a quantumness witness following the work of Alicki and van Ryn (AvR) in "A simple test of quantumness for a single system" [J. Phys. A: Math. Theor., vol. 41, 062001 (2008)]. The AvR test is designed to detect quantumness. We…

The existence of GHZ contradictions in many-qutrit systems was a long-standing theoretical question until it's (affirmative) resolution in 2013. To enable experimental tests, we derive Mermin inequalities from concurrent observable sets…

We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…

This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…

A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify the quantum advantage of an untrusted prover. That is, a quantum prover can correctly answer the verifier's challenges and…

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…

Several arguments demonstrate the incompatibility between Quantum Mechanics and classical Physics. Bell's inequalities and Greenberger-Horne-Zeilinger (GHZ) arguments apply to specific non-classical states. The Kochen-Specker (KS) one,…

We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five entangled provers, (ii) the verifier sends a classical message on O(log n) bits…

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…