Physics – Quantum Physics
Scientific paper
2011-11-14
Physics
Quantum Physics
12 pages, 3 figures
Scientific paper
Information Causality contributes to the program of deriving fundamentals of quantum theory from information theoretic principles. It puts restrictions on the amount of information learned by a party (Bob) from the other party (Alice) in a one-way communication scenario as follows. Bob receives an index b, and after a one-way communication from Alice, tries to recover a part of Alice's input. Because of the possibility of cloning, this game in its completely classical form is equivalent to one in which there are several Bobs indexed by b, who are interested in recovering different parts of Alice's input string, after receiving a public message from her. Adding a private message from Alice to each Bob, and assuming that the game is played many times, we obtain the Gray-Wyner problem for which a complete characterization of the achievable region is known. In this paper, we first argue that in the classical case Information Causality is only a single point in the dual of the Gray-Wyner region. Next, we show that despite the fact that cloning is impossible in a general physical theory, the result from classical world carries over to any physical theory provided that it satisfies a new property. This new property of the physical theory is called `Accessibility of Mutual Information' and holds in the quantum theory. We conclude that the Gray-Wyner region completely characterizes all the inequalities corresponding to the game of Information Causality. In other words, we provide infinitely many inequalities that Information Causality is only one of them. In the second part of the paper we show that Information Causality leads to a non-trivial lower bound on the communication cost of simulating a given non-local box when the parties are allowed to share entanglement. We also consider the same problem when the parties are provided with preshared randomness.
Beigi Salman
Gohari Amin
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