Experimental realization of a local-to-global noise transition in a two-qubit optical simulator

We demonstrate the transition from local to global noise in a two-qubit all-optical quantum simulator subject to classical random fluctuations. Qubits are encoded in the polarization degree of freedom of two entangled photons generated by parametric down-conversion (PDC) while the environment is implemented by using their spatial degrees of freedom. The ability to manipulate with high accuracy the number of correlated pixels of a spatial-light-modulator and the PDC spectral width allows us to control the transition from a scenario where the qubits are embedded in local environments to the situation where they are subject to the same global noise. We witness the transition by monitoring the decoherence of the two-qubit state.

Figure 1

Cartoon description of the two scenarios leading to the LtG transition. On the left: LtG transition after establishing correlations between the two environments. On the right: LtG transition as the qubits approach each other.

Figure 2

Schematic diagram of the experimental setup. A 405 nm cw laser diode generates a pump beam which passes through a half-wave plate ($\lambda /2$), a polarizing beam-splitter cube (PBS), and another half-wave plate. Then it is collimated by a telescopic system composed of two lenses $L_{t0}$ and $L_{t1}$. The beam passes through a series of compensation crystals and then it interacts with two 1-mm-long BBO crystals generating photons centered at 810 nm via PDC. Each branch passes through a lense $L$ with focal length $f$, a spatial light modulator (SLM), and a polarizer (P). Photons are finally focused into two multimode fibers through the couplers $C_1$ and $C_2$: the first is directly linked to a homemade single-photon counting module, the second is sent to a spectral selector and then to the counting module.

Figure 3

Local-to-global noise transition by translation of the realizations $\phi \left(t\right)$ for the RTN with $\gamma =0$ and $\mathrm{\Delta }\lambda =15$ nm. The time $t$ is in arbitrary units. The green dots represent the experimental data, while the blue squares are the corresponding simulations for $\left|\mathrm{Re}\right[\mathrm{\Gamma }\left(t\right)\left]\right|$. The red triangles are $\left|\mathrm{\Gamma }\right(t\left)\right|$. In the left panel we show results for $\delta =3$, i.e., the two environments are not correlated. The right panel is $\delta =0$, i.e., fully correlated environments.

Figure 4

Experimental implementation of the transition from global to local noise in the case of RTN with $\gamma =0.12$. The time $t$ is in arbitrary units. In the left column the $\delta$ shift-strategy is used. On the right column the transition is obtained by changing the spectral width $\mathrm{\Delta }\lambda$.

Figure 5

The geometry of the parametric-down-conversion scheme.

Figure 6

(top panel) The green dots represent the measured values of $V\left(h\right)$ for $\mathrm{\Delta }\lambda =15$ nm and $p=0.927$, while the blue line is the fitting sine wave. In the present case, it gives $\text{Vis}(V\left(h\right))=0.58\pm 0.03$. (central panel) The blue squares represent the value of $\text{Vis}(V\left(h\right))$ obtained by simulation for $\mathrm{\Delta }\lambda =15$ nm and $q=0.927$, while the blue dashed line is the fitting polynomial curve. The red dot is the measured value of visibility. In the present case, the extrapolated number of correlated pixel is $w_{\text{cp}}=3.1\pm 0.5$. (bottom panel) Number of correlated pixels as a function of the spectral width of the PDC: the green dots are the experimental data, the blue squares are the simulated data.