How Much Entanglement Can Be Generated between Two Atoms by Detecting Photons?

It is possible to achieve an arbitrary amount of entanglement between two atoms using only spontaneously emitted photons, linear optics, single-photon sources, and projective measurements. This is in contrast to all current experimental proposals for entangling two atoms, which are fundamentally restricted to one entanglement bit or “ebit.”

Figure 1

Schema of possible experiments for entangling two atoms. (a) Only one photon detected, but we do not know from which atom. (b) Two photons are detected, one from each atom. (c) Three photons are detected, one being supplied by the experiment (dashed line). Because of the setup, the probabilities of reaching each detector are balanced and the detectors do not distinguish between left- and right-coming photons. (d) Entangling two-photon detector “gedanken” experiment. By detecting only a range of momenta, we entangle the momenta of the atoms, $p_{1\perp }+p_{2\perp }\simeq 0$.

Figure 2

Outcome for an experiment with two atoms and three photons, as shown in Eq. (11).

Figure 3

Quantum circuit for saturating the bound of ${log}_{2}N\mathrm{ebits}$ as described in the text.