Sudden death of effective entanglement

Sudden death of entanglement is a well-known effect resulting from the finite volume of separable states. We study the case when the observer has a limited measurement capability and analyze the effective entanglement (i.e., entanglement minimized over the output data). We show that in the well-defined system of two quantum dots monitored by single-electron transistors, one may observe a sudden death of effective entanglement when real, physical entanglement is still alive. For certain measurement setups, this occurs even for initial states for which sudden death of physical entanglement is not possible at all. The principles of the analysis may be applied to other analogous scenarios, such as estimation of the parameters arising from quantum process tomography.

Figure 1

The effective entanglement of coherent states in the first measurement setup as a function of known occupations $b$ and $c$ for two values of $a$. The plot shows only nonzero effective entanglement.

Figure 2

The effective entanglement in the second measurement setup as a function of the observables $x$ and $z$. The plot shows only nonzero effective entanglement.

Figure 3

The time evolution of effective entanglement for different temperatures. Inset: Effective entanglement as a function of the measured parameter $z$.