Entanglement sharing among d qudits

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  • 10 June 2001
Abstract
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 Emax(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: Emax(3,2) = 0.550. In this paper we consider a system of d qudits and show that Emax(d,d) is greater than or equal to 1. For the special case of three particles, where we can compare qubits to qutrits (that is, 3-state particles), our results show that in a certain sense, qutrits can share entanglement better than qubits.

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