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Consider a system consisting of n d-dimensional quantum particles (qudits), and suppose that we want to optimize the entanglement between each pair. One can ask the following basic question regarding the sharing of entanglement: what is the largest possible value E₌₀ₗ (n, d) of the minimum entanglement between any two particles in the system? (Here we take the entanglement of formation as our measure of entanglement. ) For n=3 and d=2, that is, for a system of three qubits, the answer is known: E₌₀ₗ (3, 2) =0. 550. In this paper we consider first a system of d qudits and show that E₌₀ₗ (d, d) >~1. We then consider a system of three particles, with three different values of d. Our results for the three-particle case suggest that as the dimension d increases, the particles can share a greater fraction of their entanglement capacity.
Dennison et al. (Wed,) studied this question.