Observation of decoherence-induced exchange symmetry breaking in an entangled state

One of the most intriguing features of entanglement is that entangled quantum systems exhibit exchange symmetry; that is, local quantum operations on the subsystems may be interchanged without affecting the quantum state. In this work, we investigate whether the exchange symmetry is preserved for the weak (or partial collapse) measurement, a type of quantum operation, in the presence of decoherence. Demonstrated using two entangled photonic polarization qubits, the experimental results clearly show that the exchange symmetry is broken once decoherence is introduced, even though the photons still share nonzero entanglement. Our results shed light on quantum state manipulation using general quantum operations on entangled quantum states in the presence of decoherence.

Figure 1

(a) Local reversal: weak and reversal measurements are applied to the same qubit. (b) Nonlocal reversal: weak and reversal measurements are applied to different qubits. Both give the same results, fully recovering the initial quantum state $|\Phi \rangle$.

Figure 2

Alice prepares a pair of entangled qubits in state $|\Phi \rangle$ and sends them to Bob and Charlie. The qubit being sent to Charlie experiences decoherence $D$. The quantum state shared by Bob and Charlie, when $D=0$, is the same in all cases. The degeneracy, however, is lifted due to decoherence-induced exchange symmetry breaking such that there exist two classes of quantum states shared by Bob and Charlie: ${\rho }_B$ for (a) and (c) and ${\rho }_C$ for (b) and (d).

Figure 3

Alice prepares a pair of photonic polarization qubits in the maximally entangled state $|\Phi \rangle$ with $\left|\alpha \right|=1/\sqrt{2}$ and sends them to Bob and Charlie. The qubit being sent to Charlie undergoes an amplitude-damping decoherence channel. The weak measurement $W\left(p\right)$ and the reversing measurement $R\left(p_r\right)$ are applied to one of the two qubits, resulting in the four possible scenarios depicted in Fig. 2. The quantum state $\rho$ shared by Bob and Charlie is reconstructed by performing quantum state tomography.

Figure 4

(a) For $D=0.617$, concurrence vs the weak measurement strength $p$ is plotted for the experimental scenario depicted in Fig. 2. For each $p$ value, the reversing measurement strength $p_r=p+D(1-p)$ was chosen [23, 24, 26, 27]. Note that when $p=0$, $p_r$ is not zero but $p_r=D$. The experimental data clearly show that two distinct quantum states emerge due to nonzero decoherence, indicating decoherence-induced exchange symmetry breaking of weak measurement. The solid lines represent theoretical results for $C_B$ and $C_C$. The inset shows concurrence vs decoherence without weak and reversing measurements. The solid line is a theoretical result. The vertical error bars represent the statistical error of $\pm 1$ standard deviation. The horizontal error bars in the inset reflect $\pm 0.5^{\circ }$ angle errors for wave plates in the decoherence channel. (b) For different weak measurement strengths, ${\left\{p_k\right\}}_{k=1}^4=\{0,0.274,0.473,0.617\}$, the concurrence and linear entropy $S_L$ for ${\rho }_B$ and ${\rho }_C$ are plotted. The vertical and horizontal error bars represent a statistical error of $\pm 1$ standard deviation.