Figure 1

(Color online) A decay cascade where the excited state, $|u⟩$, decays to the ground state $|d⟩$, along two decay paths each emitting two photons. The left (right) branch emits two photons that are vertically, $y$ (horizontally, $x$) polarized. In (a) the intermediate level is degenerate and the cascade has perfect which path ambiguity. In (b) the degeneracy of the intermediate level is slightly broken by the detuning $\Delta =\left|E_x-E_y\right|$. This cascade has partial which path ambiguity. (c) shows how the entanglement can be distilled through spectral filtering by a window of width $w$ that erases the which path information.Reuse & Permissions

Figure 2

(Color online) The probability that distillation succeeds is an increasing function of the window $w$ shown in the red dotted curve. The entanglement of the distilled pair is a decreasing function of $w$ shown in the blue solid curve. The pair is maximally entangled at $w=0$. The plot is drawn for parameter values corresponding to biexciton decay where $\Delta /\Gamma \approx 17$.Reuse & Permissions

Figure 3

(Color online) The wave function ${\alpha }_x$ is large near the intersection of the diagonal strip, expressing total energy conservation, with the line which represents the $x$ decay path where the second photon has energy $E_x$. Similarly, the function ${\alpha }_y$ is large near the intersection of the diagonal strip with the line representing the $y$ decay path where the second photon has energy $E_y$. The cross represents a filter of narrow width. The filter collects photons that are contained in the intersection of the cross.Reuse & Permissions

Figure 4

(Color online) The phase is determined by the product of the two complex numbers $\left(k-Z_x\right)\left(k-Z_y^{\ast }\right)$. The numbers are represented as arrows pointing from $k$ to the location of the complex energies $Z_{\epsilon }$ (upper blue arrow for $Z_x$ and lower red arrow for $Z_y$). The location of $k$ is restricted by the window function $W$. In (a) the levels are detuned and the spectral window is smaller than the detuning. In (b) the levels are degenerate and in (c) the levels are detuned and the window is larger than the detuning.Reuse & Permissions

Figure 5

(Color online) The phase of $\gamma$ as a function of the (centered) normalized spectral window width $w/\Gamma$ and the detuning $\Delta /\Gamma$ for parameters appropriate to biexciton in a quantum dot. The triangular region above the diagonal represents the situation of a narrow filter where $\gamma \sim -1/2$. The triangular region below the diagonal is where the window is large, $\gamma$ is small and essentially purely imaginary. At the bottom of the figure the detuning is small and $\gamma \sim 1/2$.Reuse & Permissions

Figure 6

(Color online) The gray shapes represent the fluctuations of the cascade. The diagonal lines represent conservation of total energy and correlate the two gray shapes. They fluctuate as well. The rectangle represents the filtering. In (a) some of the events penetrate the filter and thus betray the which path ambiguity. In (b) the fluctuations do not betray the which path ambiguity and entanglement can be filtered.Reuse & Permissions

Figure 7

(Color online) The relative “weight” of the density matrix $\rho \left(s\right)$. The weight is given by $\Lambda \left(s\right)=P\left(s\right)\text{Tr}\left[W\rho \left(s\right)\right]$. The plot is renormalized to yield $\Lambda \left(0\right)=1$. The plot is obtained with the experimental values as in Sec. 7.Reuse & Permissions

Figure 8

(Color online) Comparison between the experimental results of Akopian et al. and the theory. The graph shows a theoretical calculation of the phase as a function of the window, $w$, and the detuning, $\Delta$, both in units of $\Gamma$. The calculation uses the experimentally measured parameters $w$, $\Delta$, $\Gamma$, and $s_0$. The uncertanties in these parameters result in an area (rather than a point) indicated by the error bars. The possible theoretical values of the phase are in the area which is bounded by these error bars. This values are compared to the experimentally measured phase and error, which is represented in the color bar to the left.Reuse & Permissions