Measuring higher-dimensional entanglement

We study local-realistic inequalities, Bell-type inequalities, for bipartite pure states of finite dimensional quantum systems—qudits. There are a number of proposed Bell-type inequalities for such systems. Our interest is in relating the value of the Bell-type inequality function with a measure of entanglement. Interestingly, we find that one of these inequalities, the Son-Lee-Kim inequality, can be used to measure entanglement of a pure bipartite qudit state and a class of mixed two-qudit states. Unlike the majority of earlier schemes in this direction, where the number of observables needed to characterize the entanglement increases with the dimension of the subsystems, this method needs only four observables. We also discuss the experimental feasibility of this scheme. It turns out that current experimental setups can be used to measure the entanglement using our scheme.

Figure 1

Change in the Bell-SLK function and negativity with purity for a maximally entangled two-qutrit state passed through the amplitude-damping channel.

Figure 2

Change in the Bell-SLK function and negativity with purity for a maximally entangled two-qutrit state passed through the phase-damping channel.