Experimental tests of coherence and entanglement conservation under unitary evolutions

We experimentally demonstrate the migration of coherence between composite quantum systems and their subsystems. The quantum systems are implemented using polarization states of photons in two experimental setups. The first setup is based on a linear optical controlled-phase quantum gate and the second scheme utilizes effects of nonlinear optics. Our experiment allows one to verify the relation between correlations of the subsystems and the coherence of the composite system, which was given in terms of a conservation law for maximal accessible coherence by Svozilík et al. [J. Svozilík et al., Phys. Rev. Lett. 115, 220501 (2015)]. We observe that the maximal accessible coherence is conserved for the implemented class of global evolutions of the composite system.

Figure 1

Conceptual scheme of the experimental setup with the c-phase gate adjusted at phase $\phi$.

Figure 2

Parameters of the two-photon state at the output of the c-phase gate as a function of the phase $\phi$. See text for definitions of quantities $T$ and $D$. The red curve represents theoretical dependence, $D^2+T^2=S^2=1$. The imperfection of the c-phase gate operation translates as the deviation of the experimental data from the theoretical red curve.

Figure 3

Scheme of the second experimental setup with SPDC generation of two-photon states. HWP: half-wave plate; QWP: quarter-wave plate; F: spectral filter; BDA: beam displacer assembly; BD: beam displacer; PMI: polarizing Michelson interferometer; PBS: polarizing beam splitter; FBS: fiber beam splitter; D: detector; M: motor translation.

Figure 4

Visibility of the autocorrelation function showing mutual delay of the $H$ and $V$ components of the pump pulse. The maximally entangled SPDC state is generated for the delay of $84\mu \mathrm{m}$. The situation depicted is one selected example yielding partially entangled photon pairs.

Figure 5

Antidips measured for the two-photon states starting from $|{\mathrm{\Psi }}^{-}\rangle$ for increasing delay of the $H$ and $V$ component of the pump beam. The key shows the visibility for a given delay for all measured curves.

Figure 6

Coherence of the two-photon state generated by the Kwiat-type crystal as a function of the displacement between the $H$ and $V$ components of the pump beam. Output coherence $D^2+T^2$ depicted using bars is compared with the input coherence $S_{\mathrm{in}}^2$ depicted using a Gaussian-shaped belt. The thickness of the belt represents measurement errors.