Local Quantum Measurement and No-Signaling Imply Quantum Correlations

PHYSICAL REVIEW LETTERS week ending 9 APRIL 2010

Local Quantum Measurement and No-Signaling Imply Quantum Correlations

H. Barnum,1 S. Beigi,2 S. Boixo,2,* M. B. Elliott,2 and S. Wehner2

1Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, Ontario, N2L 2Y5 Canada 2Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA (Received 26 November 2009; published 6 April 2010)

"We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. ... Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.

Quantum correlations between spacelike separated systems are, in the words of Schrodinger, ‘‘the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought’’[1]. Indeed, the increasing experimental support [2] for correlations violating Bell inequalities [3] is at odds with local realism. Quantum correlations have been investigated with increasing success [4], but what is the principle that limits them [5]?

Consider two experimenters, Alice and Bob, at two distant locations. They share a preparation of a bipartite physical system, on which they locally perform one of several measurements. This shared preparation may thereby cause the distribution over the possible two out- comes to be correlated. In nature, such nonlocal correlations cannot be arbitrary. For example, it is a consequence of relativity that information cannot propagate faster than light. The existence of a finite upper bound on the speed of information is known as the principle of no-signaling. This principle implies that if the events corresponding to Alice’s and Bob’s measurements are separated by spacelike intervals, then Alice cannot send information to Bob by just choosing a particular measurement setting. Equivalently, the probability distribution over possible outcomes on Bob’s side cannot depend on Alice’s choice of measurement setting, and vice versa. Quantum mechanics, like all modern physical theories, obeys the principle of no- signaling. ... But is no-signaling the only limitation for correlations observed in nature? ...

Conclusion.—We have shown that being locally quantum is sufficient to ensure that all nonlocal correlations between distant parties can be reproduced quantum me- chanically, if the principle of no-signaling is obeyed. This gives us a natural explanation of why quantum correlations are weaker than is required by the no-signaling principle alone; i.e., given that one can describe local physics according to quantum measurements and states, then no- signaling already implies quantum correlations.

It would be interesting to know whether our work can be used to derive more efficient tests for nonlocal quantum correlations than those proposed in [14]. Finally, it is an intriguing question whether one can find new limits on our ability to perform information processing locally based on the limits of nonlocal correlations, which we now know to demand local quantum behavior."