Entangled states of light and their robustness against photon absorption

We study how photon absorption losses degrade the bipartite entanglement of entangled states of light. We consider two questions: (i) What state contains the smallest average number of photons given a fixed amount of entanglement? (ii) What state is the most robust against photon absorption? We explain why the two-mode squeezed state is the answer to the first question but not quite to the second question.

Figure 1

Entanglement of formation as a function of the average number of photons (in both modes combined) for all bipartite states with at most one photon in each mode.

Figure 2

Entanglement of formation as a function of the average number of photons for three types of entangled coherent states (19, 20, 21).

Figure 3

Negativity as a function of average number of photons for 1000 randomly generated states whose Schmidt coefficients are equal to that of a two-mode squeezed state, with a restriction on the distance from a two-mode squeezed state, as explained in the text. The circle indicates the two-mode squeezed state.

Figure 4

Same as the previous figure, except there is no restriction on the distance to the two-mode squeezed state.

Figure 5

Negativity as a function of the average number of photons for states of the form (9).

Figure 6

Negativity as a function of the average number of photons for states with fixed pure-state negativity and entanglement of formation and at most containing three photons per mode.

Figure 7

Negativity as a function of the purity for states with fixed pure-state negativity and entanglement of formation and at most containing three photons per mode.

Figure 8

Same as Fig. 6 except for states with at most four photons.

Figure 9

Same as Fig. 7 except for states with at most four photons.