Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Quantum multi-prover interactive proof systems with limited prior entanglement
Journal of Computer and System Sciences
Consequences and Limits of Nonlocal Strategies
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Toward a general theory of quantum games
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Perfect Parallel Repetition Theorem for Quantum XOR Proof Systems
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
The complexity of the consistency and n-representability problems for quantum states
The complexity of the consistency and n-representability problems for quantum states
The Quantum Moment Problem and Bounds on Entangled Multi-prover Games
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Using Entanglement in Quantum Multi-prover Interactive Proofs
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Unique Games with Entangled Provers are Easy
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Strong NP-hardness of the quantum separability problem
Quantum Information & Computation
Entanglement in interactive proof systems with binary answers
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Polynomial-space approximation of no-signaling provers
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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Multi-party local quantum operations with shared quantum entanglement or sharedclassical randomness are studied. The following facts are established:• There is a ball of local operations with shared randomness lying within the spacespanned by the no-signaling operations and centred at the completely noisy channel.• The existence of the ball of local operations with shared randomness is employedto prove that the weak membership problem for local operations with sharedentanglement is strongly NP-hard.• Local operations with shared entanglement are characterized in terms of linearfunctionals that are "completely" positive on a certain cone K of separable Hermitianoperators, under a natural notion of complete positivity appropriate tothat cone. Local operations with shared randomness (but not entanglement) arealso characterized in terms of linear functionals that are merely positive on thatsame cone K.• Existing characterizations of no-signaling operations are generalized to the multipartysetting and recast in terms of the Choi-Jamio lkowski representation forquantum super-operators. It is noted that the standard nonlocal box is an exampleof a no-signaling operation that is separable, yet cannot be implemented by localoperations with shared entanglement.