Wiring of No-Signaling Boxes Expands the Hypercontractivity Ribbon - PowerPoint PPT Presentation

Wiring of No-Signaling Boxes Expands the Hypercontractivity Ribbon Salman A. Beigi Institute for Research in Fundamental Sciences (IPM) Tehran, Iran January 12, 2015 Joint work with Amin Gohari arXiv:1409.3665

Closed sets of nonlocal correlations

Closed sets of nonlocal correlations Foundations of Physics, Vol. 24, No. 3, 1994 Q u a n t u m N o n l o c a l i t y a s a n A x i o m S a n d u P o p e s c u t a n d D a n i e l R o h r l i c h 2 Received July 2, 1993: revised July 19, 1993 In the conventional approach to quantum mechanics, &determinism is an axiom and nonlocality is a theorem. We consider inverting the logical order, mak#1g nonlocality an axiom and indeterminism a theorem. Nonlocal "superquantum" correlations, preserving relativistic causality, can violate the CHSH inequality more strongly than any quantum correlations. What is the quantum principle? J. Wheeler named it the "Merlin principle" after the legendary magician who, when pursued, could change his form again and again. The more we pursue the quantum principle, the more it changes: from discreteness, to indeterminism, to sums over paths, to many worlds, and so on. By comparison, the relativity principle is easy to grasp. Relativity theory and quantum theory underlie all of physics, but we do not always know how to reconcile them. Here, we take nonlocality as the quantum principle, and we ask what nonlocality and relativistic causality together imply. It is a pleasure to dedicate this paper to Professor Fritz Rohrlich, who has contributed much to the juncture of quantum theory and relativity theory, including its most spectacular success, quantum electrodynamics, and who has written both on quantum paradoxes tll and the logical structure of physical theory, t2~ Bell t31 proved that some predictions of quantum mechanics cannot be reproduced by any theory of local physical variables. Although Bell worked within nonrelativistic quantum theory, the definition of local variable is relativistic: a local variable can be influenced only by events in its back- ward light cone, not by events outside, and can influence events in its i U n i v e r s i t 6 L i b r e d e B r u x e l l e s , C a m p u s P l a i n e B , C . P . 2 2 r u x e l l e s , B 5 , B o u l e v e l g i u m . a r d d u T r i o m p h e , B - 1 0 5 0 2 S c h o o l o f P h y s i c s a n d A s t r o n o m y , T e I - A v i v U n i v e r s i t y , R a m a t - A v i v , T e l - A v i v 6 9 9 7 8 I s r a e l . 3 7 9 8 2 5 / 2 4 / 3 - 4 0 0 1 5 - 9 0 1 8 / 9 4 / 0 3 0 0 - 0 3 7 9 5 0 7 . 0 0 / 0 ~ - , 1 9 9 4 P l e n u m P u b l i s h i n g C o r p o r a t i o n

Closed sets of nonlocal correlations Foundations of Physics, Vol. 24, No. 3, 1994 R E V I E W P H Y S I C A L Q u a n t u m N o n l o c a l i t y a s a n A x i l PRL 96, 250401 (2006) o m r i v i a o t T I s N i t y p l e x C o m o n i c a t i m u n o m c h C W h i i n ´thot, 1 Alain Tapp, 1 and Falk Unger 3 S a n d u o r l d P y o p W e s c n A n u t a n d t y i D a n i e l R c a l i o h r l i c h o n l o 2 o n N m i t L i ´ Allan Me n a d a Gilles Brassard, 1 Harry Buhrman, 2,3 Noah Linden, 4 Andre 7 , C a Received July 2, 1993: revised July 19, 1993 3 C 3 J e c H Q u ´ e b t r ´ e a l , M o n V i l l e , n d s e n t r e - h e r l a a l e C e N e t c c u r s m , T h 2 8 , S u s t e r d a P . 6 1 V A m d s a l , C . 0 1 8 T h e r l a n o n t r ´ e 2 4 , 1 e N e t In the conventional approach to quantum mechanics, &determinism is an axiom d e M a c h t m , T h e r s i t ´ e d e r g r e r d a U n i v e M u i A m s t I R O , a n t a g 0 G B m e n t m , P l 9 , 1 0 9 g d o m 1 e ´ p a r t e and nonlocality is a theorem. We consider inverting the logical order, mak#1g t e r d a 9 4 0 7 d K i n D n A m s B o x U n i t e e i t v a O f fi c e T W , v e r s i t P o s t B S 8 1 2 U n i C W I ) , s t o l , I L L C , i c a ( k , B r i nonlocality an axiom and indeterminism a theorem. Nonlocal "superquantum" o r m a t y W a l n I n f v e r s i t n d e e , U n i W i s k u B r i s t o l 0 6 ) v o o r y o f n e 2 0 3 t r u m correlations, preserving relativistic causality, can violate the CHSH inequality v e r s i t 2 7 J u C e n , U n i s h e d m a t i c s p u b l i c a l l y M a t h e 2 0 0 6 ; c l a s s i t o f a r c h h i b i t 4 r t m e n d 2 M t o e x D e p a more strongly than any quantum correlations. c e i v e a r t i e s ( R e t e d p e p a r a a b l e , l i k e s a c h i e v s p a c e c a l l y s t w o c l a s s i n a b l e h i n g e n t e n a n y t n g l e m r t h a p e s c u e n t a r o n g e e t , P o a n t u m a r e s t b l e . Y a t q u t i o n s p o s s i e d t h o r r e l a a t i o n l p r o v h e s e c m u n i c B e l u g h t c o m n e o u s n t h o l i g h t ) s t a n t a e i n What is the quantum principle? J. Wheeler named it the "Merlin principle" after the legendary magician who, when pursued, could change his form again and again. The more we pursue the quantum principle, the more it changes: from discreteness, to indeterminism, to sums over paths, to many worlds, and so on. By comparison, the relativity principle is easy to grasp. Relativity theory and quantum theory underlie all of physics, but we do not always know how to reconcile them. Here, we take nonlocality as the quantum principle, and we ask what nonlocality and relativistic causality together imply. It is a pleasure to dedicate this paper to Professor Fritz Rohrlich, who has contributed much to the juncture of quantum theory and relativity theory, including its most spectacular success, quantum electrodynamics, and who has written both on quantum paradoxes tll and the logical structure of physical theory, t2~ Bell t31 proved that some predictions of quantum mechanics cannot be reproduced by any theory of local physical variables. Although Bell worked within nonrelativistic quantum theory, the definition of local variable is relativistic: a local variable can be influenced only by events in its back- ward light cone, not by events outside, and can influence events in its i U n i v e r s i t 6 L i b r e d e B r u x e l l e s , C a m p u s P l a i n e B , C . P . 2 2 r u x e l l e s , B 5 , B o u l e v e l g i u m . a r d d u T r i o m p h e , B - 1 0 5 0 2 S c h o o l o f P h y s i c s a n d A s t r o n o m y , T e I - A v i v U n i v e r s i t y , R a m a t - A v i v , T e l - A v i v 6 9 9 7 8 I s r a e l . 3 7 9 8 2 5 / 2 4 / 3 - 4 0 0 1 5 - 9 0 1 8 / 9 4 / 0 3 0 0 - 0 3 7 9 5 0 7 . 0 0 / 0 ~ - , 1 9 9 4 P l e n u m P u b l i s h i n g C o r p o r a t i o n