Nonlocality is a useful quantum resource in applications such as quantum key distribution and quantum random number generation. We study nonlocality in a multi-qubit model—quantum kicked top (QKT). This system is of particular interest because it displays regular behavior, bifurcations and chaotic behavior in the classical limit, and is one of the few chaotic systems that has been experimentally realized.
First, we show that the QKT is a generator of genuine multipartite nonlocality in the pure states. We demonstrate that dynamical tunnelling—a classically forbidden phenomenon—in the QKT leads to the generation of GHZ-like maximally nonlocal states for even numbers of qubits. Second, we numerically show that the reduced states of the QKT do not violate Bell inequalities. We provide an analytical understanding of this numerical result through formulating and proving a theorem which prohibits violation of the 2-qubit Bell inequality—CHSH inequality—by any 2-qubit state that exhibits a symmetric extension. This highlights fundamental connections between two important and distinct concepts in quantum information—Bell inequalities and symmetric extension of quantum states—and provides motivation for future studies of monogamy of nonlocality.
This work has been done in collaboration with Shohini Ghose and Robert Mann.
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