Impossibility of memory in hidden-signaling models for quantum correlations.

We consider a toy model for non-local quantum correlations in which nature resorts to some form of hidden signaling (i.e., signaling between boxes but not available to the users) to generate correlations. We show that if such a model also had memory, the parties would be able to exploit the hidden-signaling and use it to send a message, achieving faster-than-light communication. Given that memory is a resource easily available for any physical system, our results add evidence against hidden signaling as the mechanism behind nature's non-local behavior

[1]  Oded Regev,et al.  Simulating Quantum Correlations with Finite Communication , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[2]  C. J. Wood,et al.  The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning , 2012, 1208.4119.

[3]  Adrian Kent,et al.  Quantum nonlocality, Bell inequalities, and the memory loophole , 2002 .

[4]  D. Bacon,et al.  Bell inequalities with auxiliary communication. , 2002, Physical review letters.

[5]  Matthew F Pusey,et al.  Theory-independent limits on correlations from generalized Bayesian networks , 2014, 1405.2572.

[6]  D. Bacon,et al.  Communication cost of simulating Bell correlations. , 2003, Physical review letters.

[7]  A. Acín,et al.  Algorithmic Pseudorandomness in Quantum Setups. , 2014, Physical review letters.

[8]  Constance van Eeden,et al.  Mathematical statistics and applications : festschrift for Constance van Eeden , 2003 .

[9]  Janos A. Csirik Cost of exactly simulating a Bell pair using classical communication , 2002 .

[10]  Yaoyun Shi,et al.  Tensor Norms and the Classical Communication Complexity of Nonlocal Quantum Measurement , 2008, SIAM J. Comput..

[11]  Michael Steiner,et al.  Towards quantifying non-local information transfer: finite-bit non-locality , 1999, quant-ph/9902014.

[12]  D. Bohm A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II , 1952 .

[13]  Stefano Pironio,et al.  Security of practical private randomness generation , 2011, 1111.6056.

[14]  R. Cleve,et al.  SUBSTITUTING QUANTUM ENTANGLEMENT FOR COMMUNICATION , 1997, quant-ph/9704026.

[15]  M. Froissart Constructive generalization of Bell’s inequalities , 1981 .

[16]  S. Popescu,et al.  Quantum nonlocality as an axiom , 1994 .

[17]  Santiago Figueira,et al.  Nonsignaling Deterministic Models for Nonlocal Correlations have to be Uncomputable. , 2017, Physical review letters.

[18]  Christian Majenz,et al.  Information–theoretic implications of quantum causal structures , 2014, Nature Communications.

[19]  Stefano Pironio,et al.  Random numbers certified by Bell’s theorem , 2009, Nature.

[20]  J. Bell On the Einstein-Podolsky-Rosen paradox , 1964 .

[21]  R Chaves,et al.  Unifying framework for relaxations of the causal assumptions in Bell's theorem. , 2014, Physical review letters.

[22]  Adrian Kent,et al.  Memory attacks on device-independent quantum cryptography. , 2012, Physical review letters.