Parallel Repetition of Entangled Games with Exponential Decay via the Superposed Information Cost

In a two-player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution. Each of them produces an output and they win the game if they satisfy some predicate on their inputs/outputs. The entangled value ω *(G) of a game G is the maximum probability that Alice and Bob can win the game if they are allowed to share an entangled state prior to receiving their inputs.

[1]  Ashwin Nayak,et al.  Bit-commitment-based quantum coin flipping , 2002, quant-ph/0206123.

[2]  Jeroen van de Graaf,et al.  Cryptographic Distinguishability Measures for Quantum-Mechanical States , 1997, IEEE Trans. Inf. Theory.

[3]  Iordanis Kerenidis,et al.  Lower Bounds on Information Complexity via Zero-Communication Protocols and Applications , 2012, SIAM J. Comput..

[4]  Carl W. Helstrom,et al.  Detection Theory and Quantum Mechanics , 1967, Inf. Control..

[5]  Iordanis Kerenidis,et al.  Optimal Bounds for Quantum Bit Commitment , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[6]  Julia Kempe,et al.  Parallel repetition of entangled games , 2011, STOC '11.

[7]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[8]  Carl W. Helstrom,et al.  Detection Theory and Quantum Mechanics (II) , 1967, Inf. Control..

[9]  Andrew Chi-Chih Yao,et al.  Informational complexity and the direct sum problem for simultaneous message complexity , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[10]  William Slofstra,et al.  Perfect Parallel Repetition Theorem for Quantum XOR Proof Systems , 2007, Computational Complexity Conference.

[11]  Hartmut Klauck,et al.  Interaction in Quantum Communication , 2006, IEEE Transactions on Information Theory.

[12]  Nisheeth K. Vishnoi,et al.  Unique games on expanding constraint graphs are easy: extended abstract , 2008, STOC.

[13]  T. Rudolph,et al.  Degrees of concealment and bindingness in quantum bit commitment protocols , 2001, quant-ph/0106019.

[14]  Ran Raz,et al.  A parallel repetition theorem , 1995, STOC '95.

[15]  Ran Raz,et al.  Direct product results and the GCD problem, in old and new communication models , 1997, STOC '97.

[16]  David Steurer,et al.  A Parallel Repetition Theorem for Entangled Projection Games , 2014, Computational Complexity Conference.

[17]  Serge Fehr,et al.  On quantum Renyi entropies: a new definition and some properties , 2013, ArXiv.

[18]  Johan Håstad,et al.  Some optimal inapproximability results , 2001, JACM.

[19]  Ravi Kumar,et al.  An information statistics approach to data stream and communication complexity , 2004, J. Comput. Syst. Sci..

[20]  Ran Raz,et al.  A Counterexample to Strong Parallel Repetition , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[21]  Julia Kempe,et al.  Unique Games with Entangled Provers are Easy , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[22]  Rahul Jain,et al.  A Parallel Repetition Theorem for Entangled Two-Player One-Round Games under Product Distributions , 2013, 2014 IEEE 29th Conference on Computational Complexity (CCC).

[23]  Thomas Holenstein,et al.  Parallel repetition: simplifications and the no-signaling case , 2007, STOC '07.

[24]  Mark Braverman.  Interactive information complexity , 2012, STOC '12.

[25]  Anup Rao,et al.  Parallel repetition in projection games and a concentration bound , 2008, SIAM J. Comput..

[26]  Mihir Bellare,et al.  Free Bits, PCPs, and Nonapproximability-Towards Tight Results , 1998, SIAM J. Comput..