Entanglement sharing among quantum particles with more than two orthogonal states
Kenneth A. Dennison, William K. Wootters · Physical Review A · 2001
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 ${E}_{\mathrm{max}}(n,d)$ 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: ${E}_{\mathrm{max}}(3,2)=0.550.$ In this paper we consider first a system of d qudits and show that ${E}_{\mathrm{max}}(d,d)>~1.$ 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.