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Whereas quantum complexity theory has traditionally been concerned with problems arising from classical complexity theory (such as computing boolean functions), it also makes sense to study the complexity of inherently quantum operations…

Quantum Physics · Physics 2021-11-12 Gregory Rosenthal , Henry Yuen

Suppose that a polynomial-time mixed-state quantum circuit, described as a sequence of local unitary interactions followed by a partial trace, generates a quantum state shared between two parties. One might then wonder, does this quantum…

Quantum Physics · Physics 2016-11-17 Patrick Hayden , Kevin Milner , Mark M. Wilde

We show that if a language $L$ admits a public-coin unambiguous interactive proof (UIP) with round complexity $\ell$, where $a$ bits are communicated per round, then the batch language $L^{\otimes k}$, i.e. the set of $k$-tuples of…

Computational Complexity · Computer Science 2025-10-23 Bonnie Berger , Rohan Goyal , Matthew M. Hong , Yael Tauman Kalai

We study a model where two opposing provers debate over the membership status of a given string in a language, trying to convince a weak verifier whose coins are visible to all. We show that the incorporation of just two qubits to an…

Computational Complexity · Computer Science 2015-07-13 Abuzer Yakaryilmaz , A. C. Cem Say , H. Gökalp Demirci

Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to…

Computer Science and Game Theory · Computer Science 2021-08-12 Jing Chen , Samuel McCauley , Shikha Singh

In this work we consider the interplay between multiprover interactive proofs, quantum entanglement, and zero knowledge proofs - notions that are central pillars of complexity theory, quantum information and cryptography. In particular, we…

Quantum Physics · Physics 2019-05-28 Alex B. Grilo , William Slofstra , Henry Yuen

We investigate the correspondence between the time and space recognition complexity of languages. For this purpose, we will code the long-continued computations of deterministic two-tape Turing machines by the relatively short-length…

Computational Complexity · Computer Science 2024-12-24 Ivan V. Latkin

We prove the following facts about the language recognition power of quantum Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more powerful than probabilistic Turing machines for any common space bound $ s $…

Computational Complexity · Computer Science 2014-01-29 Abuzer Yakaryilmaz , A. C. Cem Say

We prove that two-way probabilistic and quantum finite automata (2PFA's and 2QFA's) can be considerably more concise than both their one-way versions (1PFA's and 1QFA's), and two-way nondeterministic finite automata (2NFA's). For this…

Computational Complexity · Computer Science 2014-01-29 Abuzer Yakaryilmaz , A. C. Cem Say

The class of languages having polynomial-time classical or quantum interactive proof systems ($\mathsf{IP}$ or $\mathsf{QIP}$, respectively) is identical to $\mathsf{PSPACE}$. We show that $\mathsf{PSPACE}$ (and so $\mathsf{QIP}$) is subset…

Quantum Physics · Physics 2025-08-29 Abuzer Yakaryılmaz

Using the measurement-based quantum computation model, we construct interactive proofs with non-communicating quantum provers and a classical verifier. Our construction gives interactive proofs for all languages in BQP with a polynomial…

Quantum Physics · Physics 2013-11-08 Matthew McKague

The round complexity of interactive proof systems is a key question of practical and theoretical relevance in complexity theory and cryptography. Moreover, results such as QIP = QIP(3) (STOC'00) show that quantum resources significantly…

Quantum Physics · Physics 2024-05-29 Alex B. Grilo , Philippe Lamontagne

The class $\MIP^*$ of promise problems that can be decided through an interactive proof system with multiple entangled provers provides a complexity-theoretic framework for the exploration of the nonlocal properties of entanglement. Little…

Quantum Physics · Physics 2015-10-02 Matthew Coudron , Thomas Vidick

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 interactive protocols between a prover and a verifier, a well-known tool of complexity theory, can be used in practice to certify the correctness of automated reasoning tools. Theoretically, interactive protocols exist for all…

Logic in Computer Science · Computer Science 2023-09-07 Eszter Couillard , Philipp Czerner , Javier Esparza , Rupak Majumdar

We reconsider the concept of multi-prover commitments, as introduced in the late eighties in the seminal work by Ben-Or et al. As was recently shown by Cr\'{e}peau et al., the security of known two-prover commitment schemes not only relies…

Quantum Physics · Physics 2015-05-13 Serge Fehr , Max Fillinger

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

There are two kinds of systems that programming language researchers use for their work. Semantics engineering tools let them interactively explore their definitions, while proof assistants can be used to check the proofs of their…

Programming Languages · Computer Science 2024-09-24 Jan Liam Verter , Tomas Petricek

In recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine.…

Quantum Physics · Physics 2021-02-12 Federico Centrone , Niraj Kumar , Eleni Diamanti , Iordanis Kerenidis

Zero knowledge plays a central role in cryptography and complexity. The seminal work of Ben-Or et al. (STOC 1988) shows that zero knowledge can be achieved unconditionally for any language in NEXP, as long as one is willing to make a…

Quantum Physics · Physics 2018-03-12 Alessandro Chiesa , Michael A. Forbes , Tom Gur , Nicholas Spooner