Related papers: Quantum interactive proofs with short messages
This paper gives the first formal treatment of a quantum analogue of multi-prover interactive proof systems. It is proved that the class of languages having quantum multi-prover interactive proof systems is necessarily contained in NEXP,…
We study three variants of multi-prover quantum Merlin-Arthur proof systems. We first show that the class of problems that can be efficiently verified using polynomially many quantum proofs, each of logarithmic-size, is exactly MQA (also…
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…
In this thesis we introduce quantum refereed games, which are quantum interactive proof systems with two competing provers. We focus on a restriction of this model that we call "short quantum games" and we prove an upper bound and a lower…
We introduce two models of space-bounded quantum interactive proof systems, ${\sf QIPL}$ and ${\sf QIP_{\rm U}L}$. The ${\sf QIP_{\rm U}L}$ model, a space-bounded variant of quantum interactive proofs (${\sf QIP}$) introduced by Watrous (CC…
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…
This paper studies quantum Arthur-Merlin games, which are Arthur-Merlin games in which Arthur and Merlin can perform quantum computations and Merlin can send Arthur quantum information. As in the classical case, messages from Arthur to…
We construct a classically verifiable succinct interactive argument for quantum computation (BQP) with communication complexity and verifier runtime that are poly-logarithmic in the runtime of the BQP computation (and polynomial in the…
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…
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…
We investigate two resources whose effects on quantum interactive proofs remain poorly understood: the promise of unentanglement, and the verifier's ability to condition on an intermediate measurement, which we call post-measurement…
We propose a monotonic logic of internalised non-monotonic or instant interactive proofs (LiiP) and reconstruct an existing monotonic logic of internalised monotonic or persistent interactive proofs (LiP) as a minimal conservative extension…
We prove that QIP(2), the class of problems having two-message quantum interactive proof systems, is a subset of PSPACE. This relationship is obtained by means of an efficient parallel algorithm, based on the multiplicative weights update…
We show two results about the relationship between quantum and classical messages. Our first contribution is to show how to replace a quantum message in a one-way communication protocol by a deterministic message, establishing that for all…
Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…
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 communication holds the promise of creating disruptive technologies that will play an essential role in future communication networks. For example, the study of quantum communication complexity has shown that quantum communication…
We introduce pseudo-deterministic interactive proofs (psdAM): interactive proof systems for search problems where the verifier is guaranteed with high probability to output the same output on different executions. As in the case with…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
Secure communication requires message authentication. In this paper we address the problem of how to authenticate quantum information sent through a quantum channel between two communicating parties with the minimum amount of resources.…