Emergence of the Pointer Basis through the Dynamics of Correlations

We use the classical correlation between a quantum system being measured and its measurement apparatus to analyze the amount of information being retrieved in a quantum measurement process. Accounting for decoherence of the apparatus, we show that these correlations may have a sudden transition from a decay regime to a constant level. This transition characterizes a nonasymptotic emergence of the pointer basis, while the system apparatus can still be quantum correlated. We provide a formalization of the concept of emergence of a pointer basis in an apparatus subject to decoherence. This contrast of the pointer basis emergence to the quantum to classical transition is demonstrated in an experiment with polarization entangled photon pairs.

Figure 1

Evolution of the quantity $J_{s|\{{\Pi }_i^a\}}$ calculated for two different projectors: in the ${\sigma }_z$ basis (solid line) and in the ${\sigma }_x$ basis (dashed line).

Figure 2

Sketch of the experimental setup. Polarization entangled photons are generated in a BBO crystal. States in the form of Eq. (5) are produced using the Mach-Zhender like scheme in mode $a$, and dephasing channels are implemented with birefringent quartz crystals. Polarization state tomography is performed using the wave plates [quarter wave plate (QWP), half wave plate (HWP)] and a polarizing beam splitter.

Figure 3

Experimental results for the phase damping channel showing emergence of the classical pointer states. Blue squares and red circles correspond to the classical correlations $J_{s|\{{\Pi }_z^a\}}$ and $J_{s|\{{\Pi }_x^a\}}$, respectively. Hollow triangles correspond to $J_{s|a}^{\max }$ obtained by maximizing over all possible projective measurements. The inset shows the basis states used in obtaining $J_{s|a}^{\max }$ in the Bloch sphere, where it can be seen that the relevant basis jumps from ${\sigma }_x$ eigenstates to ${\sigma }_z$ eigenstates. The solid lines correspond to theoretical calculations from the initial $p=0$ state. Error bars were calculated using Monte Carlo simulations.