Information causality and its tests for quantum communications. I- Ching Yu Host : Prof. Chi-Yee Cheung Collaborators: Prof. Feng -Li Lin (NTNU) Prof. Li-Yi Hsu (CYCU). Outline-I. Information Causality (IC) and quantum correlations
Host : Prof. Chi-Yee Cheung
Collaborators: Prof. Feng-Li Lin (NTNU)
Prof. Li-Yi Hsu (CYCU)
The CHSH inequality
The measurement scenario
If A0, A1, B0, B1=1, -1, then Cxy=<Ax By>;
CHSH=(A0 + A1) B0 + (A0 − A1) B1; |<CHSH>| ≤ 2
Why Quantum mechanics cannot be more nonlocal?
In the communication protocol, the information gain cannot exceed the amount of classical communication.
The Random Access Code (RAC) protocol
IC says total mutual information between Bob’s guess bit β and Alice’s database is bounded by 1, i.e.,
IC is violated!
For binary quantum system
with two measurement settings per side
IC could be the physical principle to distinguish quantum correlations from the non-quantum (non-local) correlations.
Alice encodes her database by x(i+1)=a0+ai, i=0,…,k-1.
Bob encodes his given bit b as a k-1 bits string y.Multi-setting RAC protocol
The signal decay theorem
Binary symmetric channel
Binary symmetric channel
] W. Evans and L. J. Schulman, Proceedings of the 34th Annual Symposium on Foundations of Computer Science, 594 (1993).
Using the Cauchy-Schwarz inequality, we can obtain
Multi-setting Tsirelson-type inequalities
The Tsirelson inequality
It is consistent with the bound from IC !!
S. Wehner, Phys. Rev. A 73, 022110 (2006).
Multi-level RAC protocol
The signal decay theorem for di-nary channel
If , Bob can guess perfectly.
One can write down the constraints in convex optimization problem and find the quantum bound of the Bell-type function.
Moreover one can calculate the associated mutual information.
Result: The associated maximal mutual information is less than the bound from information causality.
Quantum mechanics satisfies IC
For example: the object of quantum non-locality.
Symmetric channels optimization?
Asymmetric channelsCase with non-uniform input marginal probabilities
Thanks for your listening optimization?
How to know the given joint probabilities
could be reproduced by quantum system?
A: Unless they satisfy a hierarchical quantum constraints.
The quantum constraints of joint probabilities come from the property of projection operators.
The first step of the hierarchical constraints
The second step of the hierarchical constraints
Quantum correlations satisfy IC
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