Direct measurement of concurrence for atomic two-qubit pure states

We propose a general scheme to measure the concurrence of an arbitrary two-qubit pure state in atomic systems. The protocol is based on one- and two-qubit operations acting on two available copies of the bipartite system, and followed by a global qubit readout. We show that it is possible to encode the concurrence in the probability of finding all atomic qubits in the ground state. Two possible scenarios are considered: atoms crossing three-dimensional microwave cavities and trapped ion systems.

Figure 1

Quantum circuit describing a direct measurement of the concurrence of a two-qubit pure state, where two copies are available. It involves a controlled-NOT gate, as well as ${\sigma }_y$ unitaries and other simple $R$ qubit rotations, followed by the joint measurement of the four qubits.

Figure 2

Protocol for measuring concurrence in microwave 3D cavity QED using two cavities and two Ramsey regions.

Figure 3

Four ions in a linear Paul trap that can be individually addressed, measured, and coupled to a collective motional degree of freedom to implement the protocol of Fig. 1.