Purification through Zeno-Like Measurements

A series of frequent measurements on a quantum system (Zeno-like measurements) is shown to result in the “purification” of another quantum system in interaction with the former. Even though the measurements are performed on the former system, their effect drives the latter into a pure state, irrespectively of its initial (mixed) state, provided certain conditions are satisfied.

Figure 1

Probability $P^{(\tau )}(N)$ and fidelity $F^{(\tau )}(N)$ for the model (12) when the initial state of system A, onto which $N$ measurements are performed, is a coherent state $|\alpha ⟩$ and that of system B is ${\rho }_{\mathrm{B}}\propto e^{-\omega b^{†}b/k_{\mathrm{B}}T}$ (thermal, i.e., maximally mixed). The parameters are taken to be $\omega =1$, $g=0.2$, $T=1$, $\alpha =0.5$, and $\tau =2\pi /[(\Omega +\omega )/2+\delta ]\simeq 5.24$ in units such that $\hslash =k_{\mathrm{B}}=\Omega =1$. $\tau$ is tuned so as to satisfy the condition $|{\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}|=1$ [13], and the ratio of the second largest (in magnitude) eigenvalue to the largest one ${\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is $|e^C|=\sqrt{1-(g/\delta {)}^2{sin}^2\delta \tau }\simeq 0.37$ [14].