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Noise resistance of the violation of local causality for pure three-qutrit entangled states. (English) Zbl 1302.81019

Summary: Bell’s theorem started with two qubits (spins 1/2). It is a ‘no-go’ statement on classical (local causal) models of quantum correlations. After 25 years, it turned out that for three qubits the situation is even more astonishing. General statements concerning higher dimensional systems, qutrits, etc, started to appear even later, once the picture with spin (higher than 1/2) was replaced by a broader one, allowing all possible observables. This work is a continuation of the Gdansk effort to take advantage of the fact that Bell’s theorem can be put in the form of a linear programming problem, which in turn can be translated into a computer code. Our results are numerical and classify the strength of the violation of local causality by various families of three-qutrit states, as measured by the resistance to noise. This is previously uncharted territory. The results may be helpful in suggesting which three-qutrit states will be handy for applications in quantum information protocols. One of the surprises is that the W state turns out to reveal a stronger violation of local causality than the GHZ (Greenberger-Horne-Zeilinger) state.

MSC:

81P05 General and philosophical questions in quantum theory
81P68 Quantum computation
81P40 Quantum coherence, entanglement, quantum correlations
81P15 Quantum measurement theory, state operations, state preparations
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