Gaussian discriminating strength

We present a quantifier of nonclassical correlations for bipartite, multimode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in Farace et al., [New J. Phys. 16, 073010 (2014)]. As the latter the new measure exploits the quantum Chernoff bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam splitter a factorized two-mode thermal state. For these density matrices, we study how nonclassical correlations are related with the entanglement present in the system and with its total photon number.

Figure 1

GDS of the two-mode squeezed vacuum state as a function of the squeezing parameter. In the plot we have used a set of exponentially decreasing parameters $\lambda =\frac{\pi }{2^k}$. From left to right we find the curves for $k=0,1,\cdots 6$, the optimal choice being associated with $k=0$, i.e., $\lambda =\pi$.

Figure 2

GDS with respect to logarithmic negativity $\mathcal{E}$ for a set of ${10}^6$ randomly generated two-mode squeezed thermal states with $1\le {\nu }_1={\nu }_2=\nu \le 20$ and $0\le r\le 5$. The curves corresponding to pure states (red, lower bound) and to symmetric states with $\nu =2,3,4,5,6,7$ (black dashed lines from bottom to top) are also shown. The plot is realized with $\lambda =\pi$.

Figure 3

Gaussian DS with respect to the total number of photons for a set of ${10}^6$ randomly generated two-mode squeezed thermal states with $1\le {\nu }_1={\nu }_2=\nu \le 8$ and $0\le r\le 7$. The curves corresponding to pure states (red, upper bound) and to symmetric states with $\nu =2,3,4,5,6,7$ (black dashed lines from left to right) are also shown. The blue dot-dashed line that crosses the others corresponds to the optimal GDS achieved only by means of linear mixing of thermal states. The plot is realized with $\lambda =\pi$.

Figure 4

Scheme for the state discrimination protocol on which the discriminating strength is defined. Alice and Bob prepare $n$ copies of a state, without knowing which local unitary operation $U_A$ will be applied in the following. Alice's subsystems are then modified locally by a third party (Charlie), that can choose with the same probability to (i) leave them unchanged or (ii) to apply a local rotation $U_A\in \mathcal{S}$ of his choice. The picked unitary is then communicated to Alice and Bob, that can use this information to perform the optimal joint measurement to detect whether Charlie chose option (i) or option (ii).