Protecting entanglement from finite-temperature thermal noise via weak measurement and quantum measurement reversal

In practical applications, quantum systems work in a finite-temperature environment. Quantum entanglement is inevitably destroyed by the thermal noise. Here we experimentally demonstrate the protection of entanglement on the platform of linear optics. The finite-temperature thermal noise is described by the generalized amplitude-damping channel. By performing optimal pre- and postchannel weak measurements, we successfully protect the entanglement from the generalized amplitude-damping channel. Compared with the unprotected case, the quantum coherence is recovered, and the entanglement is enhanced. The demonstrated protocol may have further applications in superconducting quantum qubits.

Figure 1

Concurrence versus $r$ with different value of $p$. The solid (dashed) lines are results with optimal (no) WMR protection. Different colors represent different values of $p$, i.e., red lines: $p=0.99$, green lines: $p=0.95$, and blue lines: $p=0.9$.

Figure 2

Concurrence versus $r$ with different values of $e_{\mathrm{mea}}$ and fixed values of $p_{\mathrm{act}}=0.95$ and $e_{\mathrm{cha}}=0$. Different colors represent different values of $e_{\mathrm{mea}}$, i.e., red lines: $e_{\mathrm{mea}}=0, p_{\mathrm{mea}}=0.95$; green lines: $e_{\mathrm{mea}}=-0.03, p_{\mathrm{mea}}=0.92$; and blue lines: $e_{\mathrm{mea}}=0.03, p_{\mathrm{mea}}=0.92$. The dashed lines are results with no protection. The solid lines are results with WMR protection, where the WM are prepared with parameter $p_{\mathrm{mea}}=p_{\mathrm{act}}-e_{\mathrm{mea}}$, which is nonoptimal for $e_{\mathrm{mea}}\ne 0$ and optimal for $e_{\mathrm{mea}}=0$.

Figure 3

Concurrence versus $r$ with different values of $e_{\mathrm{cha}}$ and fixed values of $p_{\mathrm{mea}}=0.95$ and $e_{\mathrm{mea}}=0$. Different colors represent different values of $e_{\mathrm{cha}}$, i.e., red lines: $e_{\mathrm{cha}}=0, p_{\mathrm{act}}=0.95$; green lines: $e_{\mathrm{cha}}=0.03, p_{\mathrm{act}}=0.98$; and blue lines: $e_{\mathrm{cha}}=-0.03p_{\mathrm{act}}=0.98$. The dashed lines are results with no protection. The solid lines are results with WMR protection, where the WM are prepared with parameter $p_{\mathrm{mea}}=0.95$, which is nonoptimal for $e_{\mathrm{cha}}\ne 0$ and optimal for $e_{\mathrm{cha}}=0$.

Figure 4

The experimental setup. (a) The block diagram of the experimental setup. The entangled photon pairs were combined into one beam. The photon pairs passed though the prechannel WM, the GAD channel, and the postchannel WM successively. After being separated from each other, they were detected for quantum state tomography. (b) The entanglement source. (c) The GAD channel. (d) The pre- and postchannel weak measurement. (e) The detection system. The two red circles (solid and dashed) represent the photon pair. See the main text for details.

Figure 5

Real and imaginary parts of reconstructed density matrices with $p=0.95, r=0.475$. (a) and (b) The initial entanglement state. (c) and (d) The unprotected state. (e) and (f) The protected state.

Figure 6

Concurrence versus $r$ with $p=0.95$. The red (green) solid line shows theoretical results without (with) the WMR protection. The red (green) dots represent the experimental data. Statistical errors of $\pm 1$ standard deviation are shown.