# NEEXP in MIP

@article{Natarajan2019NEEXPIM, title={NEEXP in MIP}, author={Anand Natarajan and John Wright}, journal={ArXiv}, year={2019}, volume={abs/1904.05870} }

We study multiprover interactive proof systems. The power of classical multiprover interactive proof systems, in which the provers do not share entanglement, was characterized in a famous work by Babai, Fortnow, and Lund (Computational Complexity 1991), whose main result was the equality MIP = NEXP. The power of quantum multiprover interactive proof systems, in which the provers are allowed to share entanglement, has proven to be much more difficult to characterize. The best known lower-bound…

## 14 Citations

Perfect Zero Knowledge for Quantum Multiprover Interactive Proofs

- Computer Science, Mathematics2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

The main result is that the two classes are equal, i.e., MIP* = PZK-MIP*.

Non-Locality and Zero-Knowledge MIPs

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2019

This work defines a framework in which it can quantify the simulators' non-local advantage and exhibits examples of zero-knowledge protocols that are sound against local or entangled provers but that are not sound against no-signalling provers precisely because the no- signalling simulation strategy can be adopted by malicious provers.

On the complexity of zero gap MIP

- Mathematics, Computer ScienceICALP
- 2020

This paper proves that $\mathsf{MIP}^*_0$ extends beyond the first level of the arithmetical hierarchy, and in fact is equal to $\Pi_2^0$, the class of languages that can be decided by quantified formulas of the form $\forall y \, \exists z \, R(x,y,z)$.

Quantum soundness of the classical low individual degree test

- Mathematics, Computer ScienceArXiv
- 2020

A variant of the low degree test called the low individual degree test, initially shown to be sound against multiple quantum provers in [Vid16], is analyzed and the main result is that the two-player version of this test is sound against quantumProvers.

A generalization of CHSH and the algebraic structure of optimal strategies

- Computer ScienceQuantum
- 2020

This work introduces an algebraic generalization of CHSH by viewing it as a linear constraint system (LCS) game, exhibiting self-testing properties that are qualitatively different, and gives the first example of a game that is not a self-test.

MIP* = RE

- Computer ScienceCommun. ACM
- 2021

It is proved that every problem that is recursively enumerable, including the Halting problem, can be efficiently verified by a classical probabilistic polynomial-time verifier interacting with two all-powerful but noncommunicating provers sharing entanglement.

Nonlocal games, compression theorems, and the arithmetical hierarchy

- Computer ScienceSTOC
- 2022

The Π2-completeness result is a new “gapless” compression theorem that holds for both quantum and commuting operator strategies, and explains how results about the complexity of nonlocal games all follow in a unified manner from a technique known as compression.

Self-Testing of a Single Quantum Device Under Computational Assumptions

- Computer ScienceITCS
- 2021

This work constructs a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements.

Quantum soundness of testing tensor codes

- Computer Science2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
- 2022

This work analyzes the axis-parallel line vs. point test as a two-prover game and shows that the test is sound against quantum provers sharing entanglement, implying the quantum-soundness of the low individual degree test, which is an essential component of the MIP* = RE theorem.

A doubly exponential upper bound on noisy EPR states for binary games

- Computer ScienceArXiv
- 2019

This paper provides a doubly exponential upper bound on the copies of $\psi$ for the players to approximate the value of the game to an arbitrarily small constant precision for any mono-state binary game $(G,\psi)$.

## References

SHOWING 1-10 OF 44 REFERENCES

A Multi-prover Interactive Proof for NEXP Sound against Entangled Provers

- Computer Science2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
- 2012

This work proves a strong limitation on the ability of entangled provers to collude in a multiplayer game, and shows that the correlations produced by any entangled strategy which succeeds in the multilinearity test with high probability can always be closely approximated using shared randomness alone.

Multi-Prover Quantum Merlin-Arthur Proof Systems with Small Gap

- Mathematics, Computer ScienceArXiv
- 2012

This paper studies multiple-proof quantum Merlin-Arthur (QMA) proof systems in the setting when the completeness-soundness gap is small, and shows that in this setting the proof system has the same expressive power as non-deterministic exponential time (NEXP).

Quantum proof systems for iterated exponential time, and beyond

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2018

We show that any language solvable in nondeterministic time exp( exp(⋯exp(n))), where the number of iterated exponentials is an arbitrary function R(n), can be decided by a multiprover interactive…

A Multiprover Interactive Proof System for the Local Hamiltonian Problem

- Computer Science, MathematicsITCS
- 2015

This work gives a quantum interactive proof system for the local Hamiltonian problem on n qubits in which the verifier has a single round of interaction with five entangled provers and completeness and soundness are separated by an inverse polynomial in $n.

Quantum interactive proofs with weak error bounds

- Computer Science, MathematicsITCS '12
- 2012

This paper proves that the computational power of quantum interactive proof systems, with a double-exponentially small gap in acceptance probability between the completeness and soundness cases, is…

Compression of quantum multi-prover interactive proofs

- MathematicsSTOC
- 2017

It is established that non local games are provably harder than classical games without any complexity theory assumptions and gap amplification for nonlocal games may be impossible in general.

How to delegate computations: the power of no-signaling proofs

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2013

This paper constructs a 1-round delegation scheme for every language computable in time t = t(n), and shows that the class of languages that have polynomial-time MIPs that are sound against no-signaling strategies, is exactly EXP.

Multi-prover interactive proofs: how to remove intractability assumptions

- Computer Science, MathematicsSTOC '88
- 1988

It is proved that all NP languages have perfect zero-knowledge proof-systems in this model, without making any intractability assumptions, and its properties and applicability to cryptography are examined.

Checking computations in polylogarithmic time

- Computer ScienceSTOC '91
- 1991

WJe show that every nondeterministic computational task S(Z, y), defined as a polynomial time relation between the instance x, representing the input and output combined, and the witness y can be modified to a task S such that each instance/witness pair becomes checkable in poly!ogariihmic Monte Carlo time.

Combinatorial PCPs with Efficient Verifiers

- Mathematics, Computer Science2009 50th Annual IEEE Symposium on Foundations of Computer Science
- 2009

This work provides a combinatorial construction of PCPs with verifiers that are as efficient as the ones obtained by the algebraic methods.