Perfect Commuting-Operator Strategies for Linear System Games

@article{Cleve2016PerfectCS,
  title={Perfect Commuting-Operator Strategies for Linear System Games},
  author={Richard Cleve and Li Liu and William Slofstra},
  journal={arXiv: Quantum Physics},
  year={2016}
}
Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute… 

Tsirelson’s problem and an embedding theorem for groups arising from non-local games

Tsirelson’s problem asks whether the commuting operator model for two-party quantum correlations is equivalent to the tensor-product model. We give a negative answer to this question by showing that

THE SET OF QUANTUM CORRELATIONS IS NOT CLOSED

We construct a linear system nonlocal game which can be played perfectly using a limit of finite-dimensional quantum strategies, but which cannot be played perfectly on any finite-dimensional Hilbert

3XOR Games with Perfect Commuting Operator Strategies Have Perfect Tensor Product Strategies and are Decidable in Polynomial Time

It is shown that for perfect 3XOR games the advantage of a quantum strategy over a classical strategy (defined by the quantum-classical bias ratio) is bounded, in contrast to the general3XOR case where the optimal quantum strategies can require high dimensional states and there is no bound on the quantum advantage.

Perfect Strategies for Non-Local Games

A new class of non-local games, called imitation games, in which the players display linked behaviour, and which contain as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and unique games.

Synchronous linear constraint system games

It is demonstrated that linear constraint system games are equivalent to graph isomorphism games on a pair of graphs parameterized by the linear system.

Classification and Computability for Nonlocal Games

This work attempts to relate the two models, namely XOR games and linear system games, by studying the relationships between their strategies and refutations, and tries to understand when results for one model can be transferred to the other.

Noncommutative Nullstellens\"atze and Perfect Games

The foundations of classical Algebraic Geometry and Real Algebraic Geometry are the Nullstellensatz and Positivstellensatz. Over the last two decades the basic analogous theorems for matrix and

Robust self-testing for linear constraint system games

We study linear constraint system (LCS) games over the ring of arithmetic modulo $d$. We give a new proof that certain LCS games (the Mermin--Peres Magic Square and Magic Pentagram over binary

Entanglement in Non-local Games and the Hyperlinear Profile of Groups

We relate the amount of entanglement required to play linear system non-local games near-optimally to the hyperlinear profile of finitely presented groups. By calculating the hyperlinear profile of a

Quantum and non-signalling graph isomorphisms

References

SHOWING 1-10 OF 14 REFERENCES

Characterization of Binary Constraint System Games

This work investigates a simple class of multi-prover interactive proof systems, called binary constraint system (BCS) games, and characterize those that admit a perfect entangled strategy (i.e., a strategy with value 1 when the provers can use shared entanglement) in terms of a system of matrix equations.

Binary Constraint System Games and Locally Commutative Reductions

This paper shows that several concepts including the quantum chromatic number and the Kochen-Specker sets that arose from different contexts fit naturally in the binary constraint system framework, and provides a simple parity constraint game that requires $\Omega(\sqrt{n})$ EPR pairs in perfect strategies.

Extending and characterizing quantum magic games

The Mermin-Peres magic square game is a cooperative two-player nonlocal game in which shared quantum entanglement allows the players to win with certainty, while players limited to classical

Consequences and limits of nonlocal strategies

This paper investigates various aspects of the nonlocal effects that can arise when entangled quantum information is shared between two parties, and establishes limits on nonlocal behavior by upper-bounding the values of several of these games.

Tsirelson's Problem

The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer.

TSIRELSON'S PROBLEM AND KIRCHBERG'S CONJECTURE

Tsirelson's problem asks whether the set of nonlocal quantum correlations with a tensor product structure for the Hilbert space coincides with the one where only commutativity between observables

Connes' embedding problem and Tsirelson's problem

We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP

Simple unified form for the major no-hidden-variables theorems.

  • Mermin
  • Physics
    Physical review letters
  • 1990
Two examples are given that substantially simplify the no-hidden-variables theorem of Kochen and Specker, greatly reducing the number of observables considered and requiring no intricate geometric argument, and revealing the Bell-EPR result to be the stronger of the two.

Quantum mysteries revisited again

This paper describes a device, consisting of a central source and two widely separated detectors with six switch settings each, that provides a simple gedanken demonstration of the nonclassical