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Bell inequality, Bell states and maximally entangled states for n qubits

N. Gisin·H. Bechmann-Pasquinucci
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Abstract

First, we present a Bell type inequality for n qubits, assuming that m out of the n qubits are independent. Quantum mechanics violates this inequality by a ratio that increases exponentially with m. Hence an experiment on n qubits violating of this inequality sets a lower bound on the number m of entangled qubits. Next, we propose a definition of maximally entangled states of n qubits. For this purpose we study 5 different criteria. Four of these criteria are found compatible. For any number n of qubits, they determine an orthogonal basis consisting of maximally entangled states generalizing the Bell states.

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N. Gisin, H. Bechmann-Pasquinucci. 1998-04-20. Bell inequality, Bell states and maximally entangled states for n qubits. https://doi.org/10.1016/s0375-9601(98)00516-7

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