performs a joint measurement upon all of the states. From the Holevo-Schumacher-Westmoreland theorem [@Schumacher97sendingclassical; @651037], this information rate is obtainable when $N\rightarrow \infty$.

Three cases of illumination and quantum advantage {#sec_three_cases}
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Three cases, together with three pairs of accessible information and Holevo information, are relevant for our assessment of the illumination scheme \[Fig. \[fig\_swapdiagram\](a)\] in the communication framework. They are as follows:\
*Case 1*. Quantum illumination with joint measurement: $A_q$ and $\chi_q$ are the accessible information and Holevo information, respectively, for Bob when two-mode EPR states are used as probes and idlers for illumination. Any arbitrary joint measurement over the two modes is allowed.\
*Case 2*. Quantum illumination with local measurements: $A_c$ and $\chi_c$ are the average accessible information and Holevo information for Bob with EPR state as the probe and idler, under the restriction that Bob must perform the optimal Gaussian local measurement on mode B, followed by an arbitrary local measurement on mode A. The measurement on mode B is optimal in the sense that it maximizes the amount of accessible information or Holevo information Bob receives. In this case, Bob only takes advantage of the classical correlations of the EPR state. This enables a direct comparison 