# Quantum Interactive Proofs with Competing Provers

@article{Gutoski2004QuantumIP, title={Quantum Interactive Proofs with Competing Provers}, author={Gus Gutoski and John Watrous}, journal={ArXiv}, year={2004}, volume={abs/cs/0412102} }

This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that every language having an ordinary quantum interactive proof system also has a quantum refereed game in which the verifier exchanges just one round of messages with each prover. A key part of our proof is the fact that there exists a single quantum measurement…

## 34 Citations

### Upper bounds for quantum interactive proofs with competing provers

- Computer Science20th Annual IEEE Conference on Computational Complexity (CCC'05)
- 2005

This paper uses semidefinite programming to show that many-round quantum refereed games are contained in NEXP and it follows from the symmetric nature of these games that they are also contained in coNEXP.

### Short Quantum Games

- Computer ScienceArXiv
- 2005

It is shown that certain types of quantum refereed games, including short quantum games, are decidable in deterministic exponential time by supplying a separation oracle for use with the ellipsoid method for convex feasibility.

### A study of one-turn quantum refereed games

- Mathematics
- 2020

This thesis studies one-turn quantum refereed games, which are abstract zero-sum games with two competing computationally unbounded quantum provers and a computationally bounded quantum referee. The…

### Space-efficient Simulations of Quantum Interactive Proofs

- Computer Science
- 2013

This thesis studies the quantum-enhanced version of interactive proof systems, in which each party has access to quantum computing resources and proves a PSPACE upper bound for a variant of QMA(2) that is to date the most general one known in PSPACE.

### The University of Calgary Short Quantum Games

- Computer Science

This thesis shows that certain types of quantum refereed games, including short quantum games, are decidable in deterministic exponential time by supplying a separation oracle for use with the ellipsoid method for convex feasibility.

### Annotated Bibliography

- Computer Science
- 2008

It is shown that, for any language in NP, there is a two entangled prover, one-round, interactiveProof system with single bit answers by the provers, which is currently the strongest expressive power of any known constant-bit answer, multi-prover interactive proof system.

### Multi-Prover and Parallel Repetition in Non-Classical Interactive Games

- Physics
- 2010

Since the introduction of quantum mechanics, many mysteries of nature have found explanations. Many quantum-mechanical concepts have merged with the field of computational complexity theory. New…

### Quantum Proofs

- Computer ScienceFound. Trends Theor. Comput. Sci.
- 2016

An overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define is provided.

### Toward a general theory of quantum games

- MathematicsSTOC '07
- 2007

A representation of quantum strategies is focused on that generalizes the Choi-Jamiolkowski representations of quantum, with respect to which each strategy is described by a single operations.

### Quantum Information and Variants of Interactive Proof Systems

- Computer Science
- 2011

The expressive power of quantum interactiveProof systems is exactly PSPACE, the class of problems that can be solved by a polynomial-space deterministic Turing machines and that also admit a classical interactive proof systems, and both the models are equivalent in terms of complexity-theoretic characterization.

## References

SHOWING 1-10 OF 30 REFERENCES

### Parallelization, amplification, and exponential time simulation of quantum interactive proof systems

- Computer ScienceSTOC '00
- 2000

It is proved that any polynomial-round quan tum interactiveProof system with two-sided bounded error can be parallelized to a quantum interactive proof system with exponentially small one-sided error, in which the prover and verifier exchange only 3 messages.

### Multi-Oracle Interactive Protocols with Constant Space Verifiers

- Computer ScienceJ. Comput. Syst. Sci.
- 1992

### 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.

### Making Games Short

- Economics, Computer Science
- 2006

It is shown that any EXPTIME statement can be eeciently transformed into a refereed game in which if the statement is true, the rst player wins with overwhelming probability, and if the claim is false, the second player winsWith overwhelming probability.

### On the hardness of distinguishing mixed-state quantum computations

- Computer Science20th Annual IEEE Conference on Computational Complexity (CCC'05)
- 2005

It is proved that the promise problem is complete for the class QIP of problems having quantum interactive proof systems, and is therefore PSPACE-hard.

### Making games short (extended abstract)

- Economics, Computer ScienceSTOC '97
- 1997

It is shown that any EXPTIME statement can be efficiently transformed into a refereed game in which if the statements are true, the first player wins with overwhelming probabilityy, and if the statement is false, the second player winsWith overwhelming probability.

### The Noisy Oracle Problem

- Computer Science, MathematicsCRYPTO
- 1988

A model in which a computationally bounded verifier consults with an oracle in the presence of malicious faults on the communication lines, and it is shown that a deterministic polynomial time verifier can test membership in any language in P-space, but cannottest membership in languages not in P -space, even if he is allowed to toss random coins in private.

### Cryptographic Distinguishability Measures for Quantum-Mechanical States

- Computer Science, MathematicsIEEE Trans. Inf. Theory
- 1999

This paper surveys four measures of distinguishability for quantum-mechanical states from the point of view of the cryptographer with a particular eye on applications in quantum cryptography, and obtains several inequalities that relate the quantum distinguishability measures to each other.

### A parallel repetition theorem

- Computer Science, MathematicsSTOC '95
- 1995

We show that a parallel repetition of any two-prover one-round proof system (MIP(2,1)) decreases the probability of error at an exponential rate. No constructive bound was previously known. The…

### The knowledge complexity of interactive proof-systems

- Mathematics, Computer ScienceSTOC '85
- 1985

A computational complexity theory of the “knowledge” contained in a proof is developed and examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity.